PhysicsPhysics QuestionsMotion In Straight Line Questions for CBSE Class 11th

Motion In Straight Line Questions for CBSE Class 11th

  1. The velocity of a body moving in a straight line is given by V = ( 3 x 2 + x)m/s. Find acceleration at x = 1m.
  2. Acceleration vs time graph of a body starting from rest is shown in the figure. The velocity vs time graph of the body is given by
  3. The displacement of a particle is given by x = (t – 2) 2 where x is in meters and t in seconds. The distance covered by the particle in first 4 seconds
  4. A bullet emerges from a barrel of length 1.2 m with a speed of 640 ms – 1 . Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired, is
  5. A ball is dropped onto the floor from a height of 10 m. It rebounds to a height of 5 m. If the ball was in contact with the floor for 0.01 s, what was its average acceleration during contact? (Take, g = 10 ms – 2 )
  6. Amongst the following equation of motion, which represents uniformly accelerated motion?
  7. The acceleration-time (a-t) graph for a particle moving along a straight line starting from rest is shown in figure. Which of the following graph is the best representation of variation of its velocity (v) with time (t)?
  8. A parachutist after bailing out falls 50 m without friction when parachute opens, it decelerates at 2 ms – 2 . He reaches the ground with speed of 3 m/ s. At what height did he bail out?
  9. The position x of a particle with respect to time t along X-axis is given by x = 9 t 2 – t 3 , where x is in metres and t in second. What will he the position of this particle when it achieves maximum speed along the positive x-direction?
  10. In one dimensional motion, instantaneous speed v satisfies 0 ≤ v < v 0 . Then, which of the following statement is true?
  11. In the s- t equation (s = 10 + 20 t – 5t 2 ), match the following columns and mark the correct option from the codes given below. Column I Column II (A) Distance travelled in 3 s (p) -20 units (B) Initial acceleration (q) 15 units (C) Velocity at 4 s (r) 25 units (s) -10 units Codes A B C
  12. If displacement of a particle is zero, the distance covered
  13. If the velocity of a particle is v = At + Bt 2 , where A and B are constants, then the distance travelled by it between Is and 2s is [NEET 2016]
  14. An object is moving with velocity 10 ms -1 . A constant force acts for 4 s on the object and gives it a speed of 2 ms -1 in opposite direction. The acceleration produced is
  15. The value of ΔG ° for a reaction in aqueous phase having K c = 1 , would be
  16. A ball is thrown vertically upward with a velocity u from the top of a tower . It strikes the ground with velocity 3u . The time taken by the ball to reach the ground is
  17. A particle moves along the X-axis with uniform acceleration a. It starts from rest from the origin. During its motion, the rate of change of velocity with position ( dv / dx )
  18. A car of mass m, travelling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is same for both cases. What time would be required to sop a car of mass 2 m travelling at speed v?
  19. A balloon is moving along with constant upward acceleration of I m / s 2 . A stone is thrown from the balloon downwards with speed 10 m/s with respect to the balloon. At the time of projection balloon is at height 120 m from the ground and is moving with speed 20 m/s. Find the time required to fall on the ground by the stone after the projection.
  20. An electron starting from rest has a velocity that increases linearly with time, that is, v = kt where k = 2 m/s 2 . The distance covered in the first 3 sec, will be:
  21. The velocity of a particle is v : v 0 + gt + ft 2 .If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is:
  22. Which of the following graphs represents motion with uniform velocity?
  23. When a motorcycle moving with a uniform speed 11 m/s is at a distance 24 m from a car, the car starts from rest and moves with a uniform acceleration 2 m/s 2 away from the motorcycle. If the car begins motion at t = 0, time at which the motorcycle will overtake the car is t =
  24. Two trains take 3 second to pass one another when going in opposite directions but only 2.5 second if the speed of one is increased by 50% . The time one would take to pass the other when going in the same direction at the original speed is:
  25. A parachutist steps from an aircraft, falls freely for two second, and then opens his parachute. Which of the following acceleration time (a-t) graphs best represents his downward acceleration a during the first 5 second?
  26. A vehicle travels half the distance l with speed v 1 and the other half with speed v 2 , then its average speed is [NCERT Exemplar]
  27. A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms – 1 to 20 ms – 1 while passing through a distance 135 m in t second. The value of t (in second) is
  28. A point moves in a straight line, so that its displacement x at time t is given by x 2 = t 2 + 1 . Its acceleration is
  29. A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d / 2. Neglecting subsequent motion and air resistance, its velocity v varies with the height h above the ground can be plotted as
  30. A body travelling with uniform acceleration crosses two points A and B with velocities 20ms -1 and 30ms -1 , respectively. The speed of the body at midpoint of A and B is
  31. A car starts from rest and moves with constant acceleration. The ratio of the distance covered in the nth second to that covered in n seconds is
  32. The velocity of a body depends on time according to the equation v = 20 + 0 .1 t 2 . The body is undergoing
  33. If displacement of a particle is zero, the distance covered
  34. A car moves a distance of 200 m. It covers first half of the distance at speed 60 km h -1 and the second half at speed v . If the average speed is 40 km h -1 , the value of v is
  35. A body starts from rest with a uniform acceleration of 2 m/ s 2 for 10 sec. It moves with constant speed for 30 sec, then decelerates by 4 m / s 2 to zero. What is the distance covered by the body ?
  36. A ball is dropped from a bridge 122.5 m above a river. After the ball has been falling for 2s, a second ball is thrown straight down after it. What must be the initial velocity of the second ball, so that both ball hit the water at the same time?
  37. Galileo’s experiment showed that if two bodies of unequal masses are dropped from the same height, the times required by them to reach the ground are equal. But if they are thrown the times required to reach the ground is equal to:
  38. A car moves from X to Y with a uniform speed υ u and returns to Y with a uniform speed υ d . the average speed for this round trip is:
  39. In 1.0 s, a particle goes from point A to B, moving in a semicircle of radius 1.0m. The magnitude of the average speed is:
  40. A scooter starts from rest have an acceleration of 1 ms – 2 while a car 150 m behind it starts from rest with an acceleration of 2 ms – 2 . After how much time, the car catches up with the scooter? [BHU 2012]
  41. A ball is thrown vertically upwards with some speed. It reaches two points A and B one after another such that heights of A and B are one fourth and three-fourth of the maximum height attained. If the total time of flight is T, the maximum time taken by the ball to travel from A to B, is :
  42. The displacement of a particle moving in a straight line is described by the relation S=6+12t-2t 2 . Here s in meter and t is in sec. The distance covered by the particle in first 5s is
  43. Two bodies are thrown upwards with same initial velocity 40 ms -1 with time gap 4 sec. After what time from projection of first body they will meet (g = 10 m/s 2 )
  44. A juggler throws balls vertically up in the air. He throws one up whenever the previous one is at its highest point. If he throws n balls in each second, the height to which each ball rises above the point of throw will be (g is acceleration due to gravity)
  45. A juggler throws balls vertically up in the air. He throws one up whenever the previous one is at its highest point. If he throws n balls in each second, the height to which each ball rises above the point of throw will be (g is acceleration due to gravity)
  46. The coordinates of a moving particle at time t are given by x = c t 2 and y = b t 2 . The speed of the particle is given by
  47. The position x of a particle varies with time (t) as x = a t 2 – b t 3 . The acceleration at time t of the particle will be equal to zero
  48. A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance s 1 , in the first 10 second and distance s 2 in the next 10 seconds, then
  49. A man is at a height of 100 m. He sees a car which makes an angle of π 6 with horizontal with man’s position. If the car moves to .a point where angle is π 3 , what is the distance moved by it ?
  50. The v-t graph of a moving object is given in figure. The maximum acceleration is
  51. Two cars A and B cross a point P with velocities 10m/s and 15 m/s. after that they move with different uniform accelerations and the car A overtakes B with a speed of 25 m/s. Their accelerations are in the ratio
  52. A stone falls freely under gravity. It covers distances h 1 , h 2   and   h 3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h 1 , h 2   and   h 3 is
  53. Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x P ( t ) = a t + b t 2 and x Q ( t ) = f t – t 2 . At what time do the cars have the same velocity?
  54. Three particles move in a straight line with initial velocities v 1 , v 2 a n d v 3 ( v 1 < v 2 < v 3 ) each with constant retardation ‘a’ such that the motion continues for more than one second before velocity of each particle becomes zero. If s 1 , s 2 a n d s 3 respectively be the distances travelled in the last one second before velocity becomes zero, then
  55. The position vector of a particle moving in xy plane is given by r = ( t 2 − 4 ) i ^ + ( t − 4 ) j ^ . Find velocity when particle will cross y-axis
  56. A person sitting in the ground floor of a building notices through the window, of height 1.5 m, a ball dropped from the roof of the building crosses the window in 0.1 s. What is the velocity of the ball when it is at the topmost point of the window ? ( g – 10 m / s 2 )
  57. The position vector of a particle moving in xy plane is given by r = ( t 2 − 4 ) i ^ + ( t − 4 ) j ^ .Time when it crosses y-axis
  58. A person travelling in a straight line moves with a constant velocity v 1 for certain distance ‘x’ and with a constant velocity v 2 for next equal distance. The average velocity v is given by the relation
  59. A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time t 1 if the elevator is at rest and in time t 2 if the elevator is moving uniformly. Then
  60. Ship A is travelling with a velocity of 5 k m h – 1 due east. A second ship is heading 30° east of north. What should be the speed of second ship if it is to remain always due north with respect to the first ship?
  61. A boy throws a ball straight up in the air. After the ball leaves his hand and while it is in the air, which of the following statement is true?
  62. A particle is projected vertically upward with a velocity of 40m/s. Then the length of path covered by the particle in the last second of its flight is
  63. The displacement x of a particle varies with time according to the relation . Then
  64. A motor vehicle travelled the first third of a distance s at a speed of v 1 = 10 kmph, the second third at a speed of v 2 = 20 kmph and the last third at a speed of v 3 = 60 kmph. Determine the mean speed of the vehicle over the entire distance s.
  65. If a car covers 2/5th of the total distance with v 1 speed and 3/5th of the total distance with v 2 then average speed is
  66. A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1m long and takes 1s. There is a pit on the road 11m away from the starting point. The drunkard will fall into the pit after
  67. A particle moves along a straight line such that its displacement at any time t is given by s = ( t 3 – 6 t 2 + 3t + 4)meters. The velocity when the acceleration is zero is
  68. A car moving on a straight road accelerates from a speed of 4.1 m/s to a speed of 6.9 m/s in 5.0 s. What was its average acceleration?
  69. Two cars P and Q start from a point at the same time in a straight line and their positions are represented by X P = a t + b t 2 and X q = f t – t 2 , At what time do the cars have the same velocity?
  70. A body is thrown up with a velocity ‘u’. It reaches maximum height ‘h’. If its velocity of projection is doubled the maximum height it reaches is
  71. A person in lift which ascends up with acceleration 10 m s – 2 drops a stone from a height 10 m. The time of descent is [g=10ms-2]
  72. A particle starts from the origin, goes along the x-axis to the point (20m, 0) and then returns along the same line to the point (–20 m, 0).The distance and displacement of the particle during the trip are
  73. A stone is thrown vertically from the ground. It reaches the maximum height of 500 m in 10 sec. After what time will it reach the ground from the maximum height reached ?
  74. An object reaches a maximum vertical height of 23.0 m when thrown vertically upward on the earth. How high would it travel on the moon where the acceleration due to gravity is about one sixth that on the earth ? Assume that initial velocity is the same.
  75. Which of following statements is incorrect?
  76. The correct statement from the following is
  77. Two bodies of different masses are dropped simultaneously from the top of a tower. If air resistance is same on both of them,
  78. The acceleration of a moving body can be found from
  79. A particle starts from point A moves along a straight line path with an aceleration given by a = p – qx where p,q are constants and x is distance from point A. The particle stops at point B. The maximum velocity of the paticle is
  80. A stone is thrown vertically upward with a velocity of 10 m/s. If the stone hits the ground after 5 second, the height of the tower is (Take g = 10   m / s 2 )
  81. Statement I: If air resistance is considered then time of ascent and time of descent will be different. Statement II: Magnitudes of acceleration will be different in upwards and downward motion.
  82. Velocity v of a particle moving along positive x axis as a function of time is given by v = 2t m/s. Initially the particle is to the right of the origin and 2 m away from it. Find the displacement of the particle after first 3 s.
  83. If velocity of a body is constant, Then
  84. If a particle is moving with uniform velocity, its acceleration is:
  85. A car travelling at a speed of 30 km/hr is brought to a halt in 8 m by applying brakes. If the same car is travelling at 60 km/hr it can be brought to a halt with the same braking force in:
  86. A train moving with a speed of 60 km/hr is slowed down uniformly to 30 km/hr for repair purposes during running. After this it was accelerated uniformly to reach to its original speed. If the distance covered during constant retardation be 2 km and that covered during constant acceleration be 1 km, find the time lost in the above journey.
  87. On a foggy day, two drivers spot each other when 80 m apart. They were travelling at 70 km/h and 60 km/h towards each other on the same road. Both apply brakes simultaneously which retard the cars at the rate of 5 ms -2 . Which of the following statements is correct
  88. Square of velocity and position graph of a particle is given, at point A slope is 45° then acceleration of particle at ,4 is :
  89. The velocity v of a particle as a function of its position (x) is expressed as v = c 1 – c 2 x where c 1 and c 2 are positive constants. The acceleration of the particle is
  90. A car moving with a velocity of 10 ms – 1 can be stopped by the application of a constant force F in a distance of 20 m If the velocity of the car is 30 ms – 1 , it can be stopped by this force in
  91. The displacement x of a particle varies with time t as x = a e – α t + b e β t , where a, b, α and β are positive constants. The velocity of the particle will
  92. A particle moves along a straight line. Its position at any instant is given by x = 32 t – 8 t 3 4 , where x is in metre and t is in second. Find the acceleration of the particle at the instant when particle is at rest.
  93. A point initially at rest moves along X-axis. Its acceleration varies with time as a = ( 6 t + 5 ) ms – 2 . If it starts from origin, then the distance covered in 2 s is
  94. A man is 45 m behind the bus when the bus start accelerating from rest with acceleration 2 . 5 ms – 2 . With what minimum velocity should the man start running to catch the bus?
  95. A point moves with uniform acceleration and v 1 , v 2 and v 3 denote the average velocities in the three successive intervals of time t 1 , t 2 and t 3 . Which of the following relations is correct?
  96. The displacement x of a particle in a straight line motion is given by x = 1 – t – t 2 . The correct representation of the motion is
  97. A body falling from a high Minaret travels 40 m in the last 2 seconds of its fall to ground. Height of Minaret in metre is (Take, g = 10 ms – 2 )
  98. The displacement of a particle is given by x = ( t – 2 ) 2 , where x is in metre and t in second. The distance covered by the particle in first 4 seconds is
  99. Among the four graph shown in the figure, there is only one graph for which average velocity over the time interval (0, T) can vanish for a suitably chosen T. Which one is it?
  100. The ratio of the numerical values of the average velocity and average speed of a body is always
  101. If a car covers 2/5 th of the total distance with v 1 speed and 3/5 th distance with v 2 then average speed is
  102. Two bodies A and B start from rest from the same point with a uniform acceleration of 2ms -2 . If B starts one second later, then the two bodies are separated at the end of the next second, by
  103. The motion of a particle is described by the equation v = at. The distance travelled by the particle in the first 4s is
  104. A person sitting in the ground floor of a building notices through the window of height 1.5 m, a ball dropped from the roof of the building crosses the window in 0.1 s. What is the velocity of the ball when it is at the topmost point of the window? (Take, g = 10 m/s 2 ) [NEET 2020]
  105. A person travelling in a straight line moves with a constant velocity v 1 for certain distance x and with a constant velocity v 2 for next equal distance. The average velocity v is given by the relation [NEET 2019]
  106. A particle located at x = 0, at time t = 0, starts moving along the positive X-direction with a velocity v that varies as v    =    α    x . The displacement of the particle varies with time as
  107. A car moves from A to B with a speed of 30 kmph and from B to A with a speed of 20 kmph. What is the average speed of the car ?
  108. A particle moves along a straight line such that its displacement at any time t is given by s = t 3 − 3 t 2 + 2 m The displacement when the acceleration becomes zero is
  109. If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s, it covers a distance of
  110. A body covered a distance of 5 m along a semicircular path. The ratio of distance to displacement is
  111. A body moving with uniform retardation covers 3 km before its speed is reduced to half. It comes to rest after travelling a distance of
  112. A car accelerates from rest at a constant rate of 2 m/ s 2 for some time. Then, it retards at a constant rate of 4 m / s 2 and comes to rest. What is the maximum speed attained by the car, if it remains in motion for 3 seconds ?
  113. Displacement (x) of a particle is related to time (t) as: x = at    +    bt 2 −   ct 3 where a, b and c are coonstants of the motion. The velocity of the particle when its acceleration is zero is given by
  114. Velocity is given by v = 4 t ( 1 – 2 t ) , then find the value of time at which velocity is maximum.
  115. A ball is thrown vertically upwards from the ground with a speed of 25 . 2 ms – 1 . How long does it take to reach its highest point and how high does it rise? (Take, g = 9 . 8 ms – 2 )
  116. Two bodies, A (of mass 1 kg) and B(of mass 3 kg), are dropped from heights of 16m and 25m respectively. The ratio of the time taken by them to reach the ground is:
  117. A particle moves a distance x in time t according to equation x = t + 5 − 1 . the acceleration of particle is proportional to:
  118. 2 stones are thrown form top of tower, one vertically upward and other downward with same speed. Ratio of velocity when they hit the ground is:
  119. A particle’s position as a function of time is described as y t = 2 t 2 + 3 t + 4. What is the average velocity of the particle from t = 0   t o   t = 3 sec ?
  120. A car accelerates from rest at a constant rate ‘ α ’ for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t, maximum velocity reached by the car is:
  121. Two bodies, A (of mass 1 kg) and B(of mass 3 kg), are dropped from heights of 16m and 25m respectively. The ratio of the time taken by them to reach the ground is:
  122. A particle’s position as a function of time is described as y t = 2 t 2 + 3 t + 4 . What is the average velocity of the particle from t = 0   to   t = 3 sec ?
  123. A car moves from A to B with a speed of 30 kmh – 1 and from B to A with a speed of 20 kmh – 1 . What is the average speed of the car?
  124. The acceleration of a moving body is found from the
  125. The motion of a particle along a straight line is described by equation x = 8 + 12 t – t 3 where, x is in meter and t in second. The retardation of the particle when its velocity becomes zero, is
  126. A particle moves along with X-axis. The position x of particle with respect to time t from origin is given by x = b 0 + b 1 t + b 2 t 2 . The acceleration of particle is
  127. Two bodies are thrown upwards with same initial velocity 40 ms − 1 with time gap 4 sec. After what time from projection of first body they will meet g = 10 m / s 2
  128. Assertion (A) : A body is momentarily at rest at that instant it reverses the direction Reason (R) : A body can’t have acceleration if its velocity is zero at a given instant of time
  129. A Balloon rises up with constant net acceleration 10m/s 2 . After 2s a particle drops from the balloon. After further 2s, Match the following colums (Take g=10m/s 2 ) Column-I Column-II A. Height of particle from ground P. zero B. Speed of particle Q. 10 SI units C. Displacement of particle R. 40 SI units D. Acceleration of particle S. 20 SI units A B C D 1. P R S Q 2. R P Q S 3. P S R Q 4. R P S Q
  130. A Balloon rises up with constant net acceleration 10 m / s 2 . After 2s a particle drops from the balloon. After further 2s, Match the following columns Take g = 10 m / s 2 Column-I Column-II A Height of particle from ground P zero B Speed of particle Q 10 SI units C Displacement of particle R 40 SI units D Acceleration of particle S 20 SI units A B C D 1 P R S Q 2 R P Q S 3 P S R Q 4 R P S Q
  131. The equation x =t+3 gives the variation of displacement x with time t for a particle moving along the X-axis. Which of the following is correct for the motion of the particle?
  132. A particle starts from rest from the origin and moves along the X-axis. Its position as a function of time is given by x = 6 t 2 − t 3 , here x is in meters and t is in seconds. The velocity of the particle at the equilibrium position is
  133. Consider the following statements. Choose the appropriate choice from the four choices given below the statements. A: Displacement of an object is independent of the frame of reference. B: If a body moves along a straight line, the distance and displacement are equal.
  134. The equation x =t+3 gives the variation of displacement x with time t for a particle moving along the X-axis. Which of the following is correct for the motion of the particle?
  135. A particle starting from rest and moving along a straight line has acceleration (a) given as a function of displacement (x) by the equation a = bx , where b is a positive constant. The velocity of the particle when it has a displacement d is
  136. A particle accelerates from rest at a constant rate for some time and attains a velocity of 8 m/sec. Afterwards it decelerates with the same constant rate and comes to rest. If the total time taken is 4 sec, the distance travelled is
  137. When the speed of a car is v, the minimum distance over which it can be stopped is s. If the speed becomes n v, what will be the minimum distance over which it can be stopped during same time
  138. The relation between time t and distance x is t = αx 2 + βx where α and β are constants. The retardation is
  139. A particle starts from rest. Its acceleration ( α ) versus time (t) is as shown in the figure. The maximum speed of the particle will be
  140. The water drops fall at regular interval from a tap 5 m above the ground. The third drop is leaving the tap at instant the first drop touches the ground. How far above the ground is the second drop at that instant ?
  141. An aircraft is flying at a uniform speed v m/s. If the angle subtended at an observation point on the ground by two positions of the aircraft f second apart is θ , the height of the aircraft above the ground is given by
  142. A car starting from rest, travels with uniform acceleration x and then comes to rest with uniform retardation y. If the total time of travel is t sec, the maximum velocity of the car is
  143. If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from 20 m/s to a value approaching zero at s = 30 m figure, then acceleration of the particle at s = 15 m is
  144. A particle moves with constant speed v along a regular hexagonal A B C D E F in same order (i.e., A to B, B to C, C to D, D to E, E to F and F to A). The magnitude of average velocity for its motion from A to C is
  145. A bullet fired into a wooden block loses 75% of its velocity after penetrating 15 cm into it’ How much further distance it has to penetrate to be stopped completely ?
  146. A particle is moving with uniform acceleration along a straight line ABC. Its velocity of at A and C are 5 m/s 25 m/s respectively. If BC – 2 AB, find the ratio of time of travel from A to B to that from B to C
  147. For a particle moving in a straight line, the displacement s depends on time t as t = αt 3 + βt 2 + γt + δ . The ratio of its initial acceleration to its initial velocity is
  148. A body A starts from rest with an acceleration a 1 . After 2 second, another body B starts from rest with an acceleration a 2 . If they travel equal distances in the 5th second, after the start of A, then ratio a 1 : a 2 is equal to
  149. A body starting from rest moves along a straight line with a constant acceleration. The variation of speed (v) with distance (s) is represented by the graph
  150. A small block slides without friction down an inclined plane starting from rest. Let S n be the distance travelled from time t = n -1 to t = n. Then [S n /(S n +1)] is
  151. A particle of mass m is initially situated at the point P inside a hemispherical surface of radius r as shown in figure. A horizontal acceleration of magnitude a o is suddenly produced on the particle in the horizontal direction. If gravitational acceleration is neglected, then time taken by particle to touch the sphere again is where a is the angle which OP makes with radius OC.
  152. A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity v that varies v = α X . The displacement of the particle varies with time as
  153. A car starting from rest accelerates at the rate f through a distance s, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 s, then
  154. A body sliding on a smooth inclined plane requires 4 second to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top ?
  155. A ball is dropped on to the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with floor for 0 .01 second, what is the average acceleration during contact ?
  156. If a ball is thrown vertically upwards with speed u, the distance covered during the last t second of its ascent is
  157. A person walks first 10 km north and then 20 km east, then the resultant displacement vector is
  158. A smooth square platform ABCD is moving towards right with a uniform speed v. At what angle θ must a particle be projected from A with speed u so that it strikes the point B.
  159. A man weighing 80 kg is standing on a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley along the rails at speed 1 m/s, then after 4s his displacement relative to the ground will be :
  160. A particle covers half of its total distance with speed v 1 and the rest half distance with speed v 2 . Its average speed during the complete journey is
  161. A car moves from X to Y with a uniform speed v u and returns to X with a uniform speed v d . The average speed for this round trip is
  162. For a body traveling with uniform acceleration its final velocity V= 180 – 7x where x is the distance traveled by the body in meters. Then the acceleration is
  163. A particle is moving such that its position coordinates (x,y) are (2m, 3m) at time t = 2s and (13 m, 14m) at time t = 5s Average velocity vector v av from t = 0 to t = 5 s is
  164. A metro train starts from rest and in 5 s achieves 108 km h – 1 . After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 390 m, find total time of travelling.
  165. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E . Due to the force q E , its velocity increases from 0 to 6 m s – 1 in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively
  166. If the velocity of a particle is v = A t + B t 2 , where A a n d B are constants, then the distance travelled by it between 1 s a n d 2 s is
  167. A particle is moving along x-axis as x = at 2 + bt + c ; where a, b and c are constant a = 1; b = -5 and c = 6 and t is in second. Displacement of the particle during time t = 2 to t = 3 second will be
  168. An aeroplane moving horizontally with a speed of 180 Km/hr drops a food packet while flying at a height of 500 m. the horizontal range is
  169. Two particles A and B, move with constant velocities ν 1 and ν 2 . At the initial moment their position vectors are r 1 and r 2 respectively. The condition for particles A and B for their collision is
  170. The position x of a particle with respect to time t along X-axis is given by x = 9 t 2 – t 3 where x is in metre and t in second. What will be the position of this particle when it achieves maximum speed along the + X direction?
  171. A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v ( x ) = β x – 2 n where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by
  172. A body, moving in a straight line, covers half the distance with a speed V, the remaining part of the distance was covered with a speed V 1 for half of the time and with a speed V 2 for the other half of the time. What is the average speed of the body?
  173. The displacement ‘x’ (in meter) of a particle of mass ‘m’ (in kg) moving in one dimension under the action of a force, is related to time ‘t’ (in sec) by t = x + 3 . The displacement of the particle when its velocity is zero, will be
  174. Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t 1 . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t 2 . The time taken by her to walk up on the moving escalator will be
  175. A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is 🙁 g=10 m / s 2 )
  176. A ball is dropped downwards to hit the ground at time t=0. After 1 second another ball is dropped downwards from the same point. The distance between them after 3 seconds is
  177. A person in a lift which descends down with an acceleration of 1.8 m / s 2 drops a stone from a height of 2m. The time of decent is
  178. A particle starts from rest with constant acceleration for 30sec. If it travels a distance y 1 in the first 10 sec and a distance y 2 in the next 20 sec then
  179. A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time x h y g . Find x+y.
  180. A body starts moving unidirectionally under the influence of a source of constant power. Which one of the graph correctly shows the variation of displacement (s) with time (t)?
  181. Average velocity during a journey of 240 m with uniform acceleration of 5 m/ s 2 is 40m/s. The initial velocity of the body is
  182. A body of mass 1kg is projected upward with a speed of 10 m/s. It returns to the point of projection with a speed of 8 m/s. Air resistance remains constant during the entire Journey of the body. Then maximum height attained by the body is
  183. A particle starts from rest with acceleration 2 m / s 2 . The acceleration of the particle decreases down to zero uniformly during the time interval of 4 s. The velocity of the particle after 2 s is
  184. When the speed of a car is u, the minimum distance over which it can be stopped is s. If the speed becomes nu, what will be the minimum distance over which it can be stopped during the same time?
  185. A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the nth second to the distance covered in n second is
  186. A policeman moving on a highway with a speed of 30 km h – 1 fires a bullet at thief’s car speeding away in the same direction with a speed of 192 km h – 1 . If the muzzle speed of the bullet is 150 m s – 1 , with what speed does the bullet hit the thief’s car?
  187. A ball is thrown vertically upward with a speed v from a height h metre above the ground. The time taken for the ball to hit ground is
  188. A particle, starting from origin, moves 5 m along positive x-axis upto point A. At A the particle momentarily stops and reserves its direction of motion and moves another 2m upto point B. Then displacement and distance traversed by the particle are respectively.
  189. A particle, starting from origin, moves 5 m along positive x-axis upto point A. At A the particle momentarily stops and reserves its direction of motion and moves another 2m upto point B. Then displacement and distance traversed by the particle are respectively.
  190. A particle moves a distance of 10 m along a straight line. It covers first 1/3 rd of the length of path in 2 second and rest of the length of path with velocity of 1 m/s. Then find its average velocity.
  191. A particle starts moving from origin along x-axis. Its displacement (x) after time t is given by x = t 2 m. Then the magnitude of average velocity of the particle in the interval t = 0 to t = 4 sec is
  192. A particle is moving along a straight line. It covers distance S with a velocity V. Then it covers a distance 2S with a velocity 3V in the same direction. Then magnitude of average velocity of the particle is
  193. A particle is moving along a straight line and its velocity at time t is given by v = 2t m/s. If its instantaneous acceleration at t = 2 sec is ‘a’ and average acceleration in the interval t = 0 to t = 4 sec is b , then
  194. Displacement of a particle moving along a straight line is given by x = (12t – t 2 ) m where t is time in second. Then the time after which the particle momenttarly stops is
  195. A train starts from rest from station A with constant acceleration of 2 m/s 2 . After some time it starts moving with constant retardation of 3 m/s 2 and finally stops at station B. It the separation between the stations is 1215 m, the maximum velocity attained by the train is
  196. A particle is moving along a straight line with constant acceleration. At t = 0, its velocity is 1 m/s, at t = 10 second its velocity is 5 m/s. Then its velocity at t = 20 second is
  197. Starting from rest, a particle moves with constant acceleration of 2 m/s 2 along a straight line. Then Q its displacement in the interval t = 4 sec to t = 6 sec is
  198. A particle is moving along a straight line PQR with constant acceleration. It crosses the point P with a velocity of 5 m/s and the point R with a velocity of 25 m/s. If QR = 2(PQ), find the velocity with which if crosses the point Q
  199. A particle, starting from rest moves along x-axis for some time with constant acceleration of 2 m/s 2 . After some time it starts moving with constant retardation of 3 m/s 2 and stops. If total time of travel is 20 second, its maximum velocity is
  200. A particle starts moving from x-axis and continues to move along x-axis. Its velocity at time t is V = t 3 m/s. Then its average velocity in the internal t = 0 to t = 2 sec is
  201. A body is thrown vertically upward from a point on ground. The body reaches a height above the ground at times t = 3 sec and t = 6 sec. Then velocity of projection is
  202. A body is projected vertically upward with a velocity of 30 m/s. It crosses a horizontal line AB at a height above the ground, first during its upward journey and then during its downward journey, in a time interval of 5 sec. Then height of the line AB ‘h’ is equal to
  203. A particle is moving along a straight line. At first and fifth second its velocities are 1 m/s and 4 m/s respectively. Then initial velocity of the particle is
  204. A body is projected vertically upward with a velocity ‘u’. When it arrives at half of its maximum height, its velocity becomes V. Then u v is equal to
  205. A body is released from the top of a tower. In the last second of its free fall from rest, it covers the lower half of the height of the tower. Then the time of flight of the body is
  206. A train starting from rest moves with constant acceleration of 2 m/s 2 for 5 minutes. Then it suddenly increases its acceleration from 2 m/s 2 to 4 m/s 2 and moves for another 10 minutes. Then average acceleration of the train is
  207. An object is projected vertically upward with velocity u from the bottom of a tower of height H. At the same time another object is released from rest from the top of the tower. They are moving along the same vertical line. The objects will collide in air if
  208. Acceleration (a) – time (t) graph of a particle moving along a straight line is a shown in figure. If initial velocity of the particle is 4 m/s, velocity at the end of 4 th second is
  209. Displacement of a particle moving along straight line is given by x = ( 4 t 2 – 3 t + 8 ) m m where t is time in second. Then acceleration of the particle at t = 1 second is (3) 4 m/s 2
  210. Velocity of a particle moving along a straight line is given by V = 2x 2 m/s where x is displacement in metre. Then acceleration of the particle when x = 2m is
  211. A body is projected vertically upward with a velocity of 20 m/s from a point on ground. It g = 10 m/s 2 , average speed of body during the course of its flight is
  212. A particle starts from origin with a velocity of 10 m/s and continues to move along positive x-axis with uniform retardation of 5 m/s 2 . Then length of path traversed by the particle when it cross the origin again is
  213. A particle is initially at rest at the origin. It starts moving along positive x-axis with acceleration a = 2t m/s 2 where t is time in second. Then velocity of the particle at t = 4 second is
  214. A particle is moving along a straight line with an acceleration a = 3t 2 m/s 2 where ‘t’ is time in second. Initial velocity of the particle is zero. Then the displacement of the particle at t = 2 sec is
  215. Displacement (x) – time (t) graph of a particle moving along a straight line is shown in figure. Then velocity of the particle is
  216. \vec{u}\,=\,2\hat{i} A body is projected vertically upward with a velocity of 10 m/s from the top of a tower. At the same time a second body is projected vertically downward with a velocity of 5 m/s . Then velocity of the second body, relative to the first one after 3 second.will be (3) 16 m/s
  217. A stone is thrown vertically upward with an initial velocity v 0 . The distance travelled in time 4 v 0 3 g is
  218. Two particles A and B are initially at rest at the origin. They simultaneously start moving along positive x-axis, ‘A’ with constant velocity u and B with constant acceleration ‘a’. Then find the separation between the particles when their relative velocity is zero.
  219. Velocity of a particle moving with uniform acceleration at some instant is 10 m/s. After 5 seconds from that instant its velocity becomes 20 m/s. Its velocity 3 seconds before the instant is
  220. A particle starts from rest at the origin and continues to move along positive x-axis with acceleration 2   m / s 2 . After some time it starts moving with constant retardation 3   m / s 2 and finally stops at a point on x-axis. If total time of journey of the particle is 10 sec, find the time during which the particle is accelerated.
  221. Acceleration of a particle moving along a straight line is changing with time according to the graph shown in figure. Initially the particle was at rest. Its maximum velocity is
  222. A particle starts moving from rest from the origin with constant acceleration of 1    m / s 2 and continues to move along X-axis. After sometime it starts moving with constant retardation of 2    m / s 2 and finally stops at a point. If the total distance traversed by the particle is 12 m, its maximum velocity is
  223. A truck is moving with a velocity of 10 m/s. A person on the truck, projects a ball vertically upward with a velocity of 10 m/s. When the person catches the ball again, the truck covers a distance g = 10    m / s 2
  224. A particle moves along a straight line path. After some time it come to rest. The motion is with constant acceleration whose direction with respect to the direction of velocity is
  225. The definition of average velocity is
  226. In one dimensional motion, instantaneous speed v satisfies ( 0 ≤ v ≤ v 0 )
  227. The displacement of a particle moving along x-axis is given by : x = a + bt + ct 2 The acceleration of the particle is
  228. A particle moves along a straight line such that its displacement at any time t is given by s = t 3 – 6 t 2 + 3 t + 4 The velocity when its acceleration is zero, is
  229. The relation between time and distance is t = αx 2 + βx , where α and β are constants . The retardation is
  230. A car completes its journey in a straight line in three equal parts with speeds v 1 , v 2 and v 3 respectivley . The average speed v is given by
  231. A car covers 1 3 part of total distance with a speed of 20km hr -1 and second 1 3 part with a speed of 30 km hr -1 and the last 1 3 part with a speed of 60 km hr -1 . The average speed of the car is
  232. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is :
  233. A particle moves along x axis in such a way that its coordinate x varies with time t according to the equation x = A 0 – A 1 t + A 2 t 2 . The initial velocity of the particle is
  234. Th displacement x of a particle varies with time t as x = ae – αt + be βt , where a, b, α and β are positive constants. The velocity of the particle will
  235. A car moves from X to Y with a uniform speed v u and returns to Y with a uniform speed v d . The average speed for this round trip is:
  236. A car moves from X to Y with a uniform speed v u and returns to Y with a uniform speed v d . The average speed for this round trip is
  237. A body is moving with uniform velocity of 8 ms – 1 . When the body just crossed another body, the second one starts and moves with uniform acceleration of 4 ms – 2 . The distance covered by the second body when they meet is:
  238. A body is moving with uniform velocity of 8 ms – 1 . When the body just crossed another body, the second one starts and moves with uniform acceleration of 4 ms – 2 . The time after which two bodies meet will be:
  239. A police party is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motor cycle. When he is at a distance x from the jeep, he accelerates from rest at a constant rate α . Which of the following relations is true, if the police is able to catch the dacoit?
  240. A moving car possesses average velocities of 5 ms – 1 , 10 m/s and 15 m/s in the first, second and third seconds respectively. What is the total distance covered by the car in these three seconds?
  241. A particle is moving in a straight line with initial velocity u and uniform acceleration f. If the sum of the distances travelled in t th and ( t + 1 ) th seconds is 100 cm , then its velocity after t seconds , in cm / s , is
  242. You drop a ball from a window located on an upper floor of a building. It strikes the ground with speed v. You now repeat the drop, but your friend down on the ground throws another ball upward at the same speed v, releasing her ball at the same moment that you drop yours from the window. At some location, the balls pass each other. This location is
  243. A train normally travels at a uniformly speed of 72 km/h on a long stretch of straight level track. On a particular day, the train was forced to make a 2.0 minute stop at a station on this track. If the train decelerates at a uniform rate of 1.0 m / s 2 and accelerates at a rate of 0.50 m / s 2 , how much time is lost in stopping at the station?
  244. The position x of a particle varies with time t as x = a t 2 – b t 3 . The acceleration of the particle will be zero at time t equal to
  245. Two cars start in a race with velocities u 1 and u 2 and travel in a straight line with acceleration ‘ α ’ and β . If both reach the finish line at the same time, the range of the race is
  246. A train takes t sec to perform a journey. it travels for t/n sec with uniform acceleration then for ( n – 3 n ) t sec with uniform speed v and finally it comes to rest with uniform retardation. Then average speed of train is
  247. The distance travelled by a body moving along a line in time t is proportional to t 3 . The acceleration – time (a, t) graph for the motion of the body will be
  248. A car travelling with a speed 126 KMPH along a straight line comes to rest after travelling a distance 245 m with uniform retardation. The time taken by the car to come to rest, in second is
  249. A motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He next continues north, travelling 130 km in 2.00 hours. What is his total displacement
  250. A person walks along a straight road from his house to a market 2.5kms away with a speed of 5 km/hr and instantly turns back and reaches his house with a speed of 7.5 kms/hr. The average speed of the person during the time interval 0 to 50 minutes is (in m/sec)
  251. A car moving with a speed of 50 km/hr can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr the minimum stopping distance is
  252. A particle starts moving from rest with uniform acceleration. It travels a distance x in the first 2 sec and a distance y in the next 2 sec. Then
  253. If the particle is moving along a straight line given by the relation x = 2 – 3t + 4 t 3 where x is in cms., and t in sec. Its average velocity during the third sec is ?
  254. A bullet fired into a fixed target loses half of its velocity in penetrating 15 cm. How much further it will penetrate before coming to rest?
  255. For a body travelling with uniform acceleration, its final velocity is , where x is the distance travelled by the body. Then the acceleration is
  256. If the velocity of a particle is v = At + B t 2 , where A and B constants, then the distance travelled by it between 1s and 2s is.
  257. A bus starts from rest with a constant acceleration of 5 m/ s 2 . At the same time a car travelling with a constant velocity 50 m/s. The bus overtakes and passes the car. How fast is the bus travelling when they are side by side?
  258. Two trains are each 50m long moving parallel towards each other at speeds 10 m/s and 15 m/s respectively, at what time will they pass each other?
  259. The position of an object moving along x-axis is given by x = a + bt 2 where a = 8.5 m, b = 2.5 ms –2 and t is measured in seconds. Then which of the following is true ?
  260. A police van moving on a highway with a speed of 30 K m h – 1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h – 1 . If the muzzle speed of the bullet is 150 m s – 1 , The speed with which the bullet hit the thief’s car is
  261. A body starting with a velocity ‘v’ returns to its initial position after ‘t’ second with the same speed, along the same line. Average acceleration of the particle is
  262. A student starts from his house with a speed 2kmph and reaches his college 3 min late. Next day he increases his speed by 1kmph and reaches college 3 min earlier. The distance between his house and college is
  263. A body falls from 80 m. Its time of descent is [g = 10 ms -2 ]
  264. Two bodies whose masses are in the ratio 2:1 are dropped simultaneously at two places A and B where the accelerations due to gravity are g a and g b respectively. If they reach the ground simultaneously, the ratio of the heights from which they are dropped is
  265. A body is dropped from a height 122.5 m. If it is stopped after 3 seconds and again released, the further time of descent is (g=9.8 m/ s 2 )
  266. The ratio of times taken by freely falling body to cover first metre, second metre,.. is
  267. A ball dropped on to the floor from a height of 10 m rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.02s, its average acceleration during contact is
  268. A splash is heard 3.12s after a stone is dropped into a well 45 m deep. The speed of sound in air is [g = 10 ms -2 ]
  269. A body is projected vertically upward with a velocity of 50 m/s . Then the ratio of distances travelled in the first second of upward motion to first second of downward motion is (Take g =10 m / s 2 ).
  270. A body is projected vertically up with u. Its velocity at half its maximum height is
  271. A stone is projected vertically up from the ground with velocity 40 ms –1 . The interval of time between the two instants at which the stone is at a height of 60 m above the ground is (g = 10 ms –2 ).
  272. A body is projected vertically up with velocity 98 m s – 1 . After 2 s if the acceleration due to gravity of earth disappears, the velocity of the body at the end of next 3 s is
  273. A stone is thrown vertically up from a bridge with velocity 3 m s – 1 . If it strikes the water under the bridge after 2 s, the bridge is at a height of (g = 10 m s – 2 ).
  274. A bullet fired vertically up from the ground reaches a height 40 m in its path from the ground and it takes further time 2 seconds to reach the same point during descent. The total time of flight is (g = 10 m s – 2 )
  275. A boy throws n balls per second at regular time intervals. When the first ball reaches the maximum height he throws the second one vertically up. The maximum height reached by each ball is
  276. A body is projected up with velocity u. It reaches a point in its path at times t 1 and t 2 seconds from the time of projection. Then ( t 1 + t 2 ) is
  277. How long does it take a brick to reach the ground if dropped from a height of 65 m? What will be its velocity just before it reaches the ground ?
  278. A helicopter is ascending vertically with a speed of 8.0 ms -1 . At a height of 12 m above the earth, a package is dropped from a window. How much time does it take for the package to reach the ground ?
  279. At time t = 0, two bodies A and B are at the same point. A moves with constant velocity V and B starts from rest and moves with constant acceleration a. Relative velocity of B with respect to A when the bodies meet each other is
  280. The displacement time graphs of two moving particles 1 and 2 make angles of 30 o and 45 o with the x-axis. The ratio of velocity of 1 to that of 2 is.
  281. The displacement of a particle moving along the x-axis is given by equation x = 2 t 3 – 21 t 2 + 60t + 6. The possible acceleration of the particle when its velocity is zero is
  282. Two bodies of different masses are dropped simultaneously from the top of a tower. If air resistance is proportional to the mass of the body,
  283. A body falls freely from a height ‘h’. Its average velocity when it reaches earth is
  284. A car is moving along a straight line OP as shown in the figure. It moves from O to P in 18 s and returns from P to Q in 6 s. Which of the following statements is not correct regarding the motion of the car A : The average speed of the car in going from O to P and come back to Q is 20m s – 1 B : The average velocity of the car in going from O to P and come back to Q is 15m s – 1
  285. A body falls freely from a height ‘h’ after two seconds if we assume that gravity disappears instead of getting reversed, the body
  286. A freely falling body traveled xm in n th second distance travelled in (n – 1) th second is
  287. A body is projected up with a velocity 50ms -1 after one second if accelaration due to gravity disappears then body
  288. From the top of a tower a body A is thrown up vertically with velocity u and another body B is thrown vertically down with the same velocity u. If v A and v B are their velocities when they reach the ground and t A and t B are their times of flight, then
  289. Following are four different relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one (s).
  290. A body thrown vertically up with velocity u reaches the maximum height h after T seconds. Which of the following statements is true ?
  291. The displacement of a particle as a function of time is shown in the figure. The figure shows that
  292. From the top of a tower two bodies are projected with the same initial speed of 40 ms –1 , first body vertically upwards and second body vertically downwards. A third body is freely released from the top of the tower. If their respective times of flights are T 1 , T 2 and T 3 identify the correct descending order of the times of flights
  293. The velocity-time graph of a particle in onedimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval t 1 to t 2 ?
  294. A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time. (Take acceleration in the backward direction as positive)
  295. Figures (i) and (ii) below show the displacement – time graphs of two particles moving along the x – axis. We can say that
  296. The displacement – time graph of moving particle is shown below. The instantaneous velocity of the particle is negative at the point.
  297. The area under acceleration-time graph gives
  298. Consider the motion of the tip of the minute hand of a clock. In one hour a) the displacement is zero b) the distance covered is zero c) the average speed is zero d) the average velocity is zero
  299. A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if the air resistance is not ignored?
  300. An object may have a) varying speed without having varying velocity b) varying velocity without having varying speed c) nonzero acceleration without having varying velocity d) nonzero acceleration without having varying speed.
  301. The velocity of a particle is zero at t = 0. a) The acceleration at t = 0 must be zero. b) The acceleration at t = 0 may be zero. c) If the acceleration is zero from t = 0 to t = 10 s, the speed is also zero in this interval. d) If the speed is zero from t = 0 to t = 10 s the acceleration is also zero in this interval.
  302. Wind is blowing to east along two parallel railway tracks. Two trains moving with the same speed in opposite direction have the steam track of one double that of the other. The speed of each train is
  303. Velocity (v) versus displacement (x) plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration (a) as a function of displacement (x) is
  304. Initial height of the body from the ground can be calculated by using the formula h = – ut + (1/2)gt 2 then a) A body projected vertically with velocity ‘u’ from the top of tower, reaches the ground in ‘t’ sec. b) A body dropped from a balloon moving up with uniform velocity, reaches the ground in ‘t’ sec c) A body dropped from a helicopter moving up with uniform velocity, reaches the ground in ‘t’ sec d) A body projected vertically from the ground reaches the ground in ‘t’ sec.
  305. In one dimensional motion, instantaneous speed V satisfies 0 ≤ V < V 0
  306. Velocity of the body on reaching the ground is same in magnitude in the following cases a) a body projected vertically from the top of tower of height ‘h’ with velocity ‘u’ b) a body thrown down wards with velocity ‘u’ from the top of tower of height ‘h’ c) a body projected horizontally with a velocity ‘u’ from the top of tower height ‘h’ d) a body dropped from the top tower of height ‘h’
  307. A train moving at a constant velocity of 54 km/hr moves east wards for 30 minutes, then due north with the same speed for 40 minutes. What is the average velocity of the train during this run? (in km/hr)
  308. A train of 150 metre length is going towards east direction at a speed of 10 m/s. A parrot flies at the speed of 5 m/s towards west direction parallel to the railways track. The time taken by the parrot to cross the train is
  309. When two bodies approach each other with the different speeds, the distance between them decreases by 120 m for every one minute. If they are moving in same direction, the distance between them increases by 90 m for very one minute. The speeds of the bodies are
  310. A particle starts from rest with constant acceleration of 2   m / s 2 along a straight line. After some time it starts moving with constant retardation of 4   m / s 2 and finally stops. If total time of journey is 24 sec, the maximum velocity attained by the particle is
  311. A particle starts moving from rest along a straight line with constant acceleration of 2 m / s 2 . After 4 second it starts moving with constant retardation of 4 m / s 2 and finally stops. Then total distance covered by the particle is
  312. Two particles at a distance 5 m apart, are thrown towards each other on an inclined smooth plane with equal speeds ‘v’.One particle is projected up the plane and the other is projected down the plane . Inclined plane is inclined at an angle of 30 0 with the horizontal. It is known that both particle move along the same straight line. The particles collide at the point from where the lower particle is thrown. Find the value of v. [take g = 10 m / s 2 ]
  313. The position of a particle moving rectilinearly is given by x = t 3 – 3 t 2 – 10 . Find the distance travelled by the particle in the first 4 seconds starting from t = 0.
  314. One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance (s) between the two stones varies with time (r) as (before either stone hits the ground)
  315. The velocity of a particle moving along X axis changes with position as per the equation given by v 2 = ( x 2 + 2 x – 1 ) . Find the instantaneous tangential acceleration of the particle at x = 1m.
  316. A point moves with uniform acceleration and v 1 , v 2 and v 3 denote the average velocities in three successive intervals of time t 1 , t 2 and t 3 . Which of the following relations is correct?
  317. Tripling the speed of a motor car multiplies the distance needed for stopping it by:
  318. Body A starts from rest with an acceleration a 1 . After two seconds another body B starts from rest with an acceleration a 2 . If they travel equal distances in fifth second. The ratio a 1 : a 2 will be equal to:
  319. A particle moving with a uniform acceleration along a straight line covers distances a and b in successive intervals of p and q second. The acceleration of the particle is:
  320. A particle located at x = 0 at time t = 0,starts moving along the positive, x-direction with a velocity ‘v’ that varies as v = α x ,. The displacement of the particle varies with time as:
  321. The deceleration experienced by a moving motorboat, after its engine is cut-off is given by dv dt = – kv 3 where k is constant. If v o is the magnitude of velocity at cut-off, the magnitude of velocity at time ‘t’ after the cut-off is:
  322. A particle is moving such that its position vector varies with time as r = 1 – αt t A where α and A are constant quantities. At t = 0, the particle is at a position O. At some later instant ‘t 0 ‘ , the particle is again at O. Velocity of the particle at the instant t 0 is:
  323. A car moving with a speed of 50 km/h, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is :
  324. Fine the correct statement out of the following: (i) if acceleration = 0, motion is uniform. (ii) if acceleration = constant, acceleration is uniform but motion not. (iii) if acceleration ≠ constant, both acceleration and motion are not uniform. (iv) if acceleration = constant, both acceleration and motion are uniform.
  325. If a body is accelerating : (i) it may speed up (ii) it may speed down (iii) it may move with same velocity (iv) it may move with same speed
  326. Displacement (x) of a particle is related to time (t) as; x = at +bt 2 -ct 3 where a, b and c are constant of the motion. The velocity of the particle when its acceleration is zero, is given by:
  327. The acceleration a (in ms -2 ) of a body, starting from rest varies with time t (in s) following the equation a = 3t + 4. The velocity of the body at time t = 2 s will be
  328. For a particle displacement time relation is t = x + 3 . Its displacement when its velocity is zero :
  329. A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time average velocity is:
  330. Motion of a particle is given by equation g = (3t 3 + 1t 2 + 14t + 8) m. The value of acceleration of the particle at t = 1 sec is :
  331. A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t – t 3 . How long would the particle travel before coming to rest ?
  332. A particle starts its motion from rest under the action of a constant force, if the distance covered in first 10 seconds is S 1 and that covered in the first 20 seconds is S 2 , then:
  333. The distance x travelled by a particle in time t is given by t = 2x 2 +3x.If ‘v’ is the velocity, then acceleration will be :
  334. A particle is moving such that its position coordinates (x, y) are (2m,3m)at time t=0 (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5 s. Average velocity vector v av from t =0 to t = 5s is:
  335. A particle of unit mass undergoes one-dimensional motion such that its velocity varies according t v x = βx – 2 n where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by :
  336. If the velocity of a particle is u = At + Bt 2 ,where A and B ate constants, then the distance travelled by it between 1s and 2s is :
  337. Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t 1 . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t 2 . The time taken by her to walk up on the moving escalator will be :
  338. Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x P (t)= at+bt 2 and x Q (t)= ft-t 2 . At what time do the cars have the same velocity
  339. Two bodies of different masses say 1 kg and 5 kg are dropped simultaneously from a tower. They will reach the ground:
  340. If a light and a heavy body are released from same height:
  341. A body of mass 500 kg is thrown vertically upwards with a speed of 200 m/s. On the return journey its speed at the starting point will be:
  342. Two bodies of different masses m a and m b are dropped from two different heights, viz; a and b. The ratio of time taken by the two to drop through these distances, is:
  343. A body let fall from the top of a building reaches the ground in 3 s. The height of the building is:
  344. A ball is released from the top of height h meter. It takes T second to reach the ground. Where is the ball at the time T/2 sec?
  345. An object is projected upwards with a velocity of 4.9 m/s. It will strike the ground in approximately
  346. A stone is thrown vertically upwards with a velocity of 98m/s. Its velocity will be zero after (g = 9.8m/s) 2
  347. A stone is thrown upwards from the surface of the earth with an initial speed of 5 m/s. The stone comes to rest at a height of (g = 1000 dyne/g)
  348. A boy throws balls into air. He throws one, whenever the previous one is at its highest point. How high do the balls rise if he throws one ball each sec
  349. A pebble is thrown vertically upwards from a bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. The height of the bridge is:
  350. A body falls from rest freely under gravity with an acceleration of 9.8 m/s 2 . Neglecting air resistance, the distance travelled by the body during the third second of its motion will be
  351. A ball is thrown vertically upwards with a speed of 10 m/s from the top of a tower 200 m high and another is thrown vertically downwards with the same speed simultaneously. The time difference between them in reaching the ground (in s) is : (g = 10 m/s) 2
  352. A stone is dropped into a lake from a tower 500 m high. The sound of the splash will be heard by a man on the tower after:
  353. A ball is released from the top of a tower of height h m. It takes T s to reach the ground. What is the position of the ball in T 3 s ?
  354. With what speed should a body be thrown upwards so that the distances traversed in the 5th second and 6th second are equal ?
  355. A packet is released from a balloon which is rnoving upward when the balloon is at a height 200 m above ground. The packet reaches the ground in 8 sec. Speed of the balloon when the packet is released, is: (take g = 10 m/s) 2
  356. A stone dropped from the top of a tower travels 5 9 of the height of tower during the last second of fall. Height of the tower is: (take g = 10 m/s 2 )
  357. A packet is dropped from a balloon that is moving upward when the balloon is at a height 60 m above ground. If the speed of the balloon at the moment of release of packet is 5 m/s, time taken by the packet to reach ground will be: (take g = 10 m/s 2 )
  358. An object is dropped from the top of a tower. It travels a distance ‘x’ in the first second of its motion and a distance ‘7x’ in the last second. Height of the tower is (take g= 10 m/s 2 )
  359. 2 stones are thrown from top of tower, one vertically upward and other downward with same speed. Ratio of velocity when they hit the ground is
  360. From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically) with same speed. If v A and v B are their respective velocities on reaching the ground, then
  361. A body starts falling from height ‘h’ and travels distance h 2 during last second of motion then time of flight is (in second ):
  362. If a ball is thrown vertically upwards with speed u, the distance covered during the last ‘t’ seconds of its ascent is :
  363. Two bodies, A (of mass 1 kg) and B (of mass 3 kg), are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is :
  364. A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10ms -2 , the velocity with which it hits the ground is :-
  365. A ball is thrown vertically upward. [t has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise ? (take g = 10 m/s 2 )
  366. A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by:
  367. A stone falls freely under gravity. It covers distances h 1 , h 2 and h 3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h 1 , h 2 and h 3 is :
  368. A particle is projected vertically upward with speed u = 10 m/s. During its journey air applies a force of -0.2v 2 on the particle. What is the maximum height attained by the particle [m = 2kg]
  369. Which of the following figures represents the motion of a body moving in a straight line under constant acceleration?
  370. The velocity versus time curve of a moving point is shown in Figure. The retardation is:
  371. An object is dropped from rest. Its velocity versus displacement graph is :
  372. A particle starts from rest. a(m/s 2 ) Its acceleration (a) versus time (r) is as shown in the Figure. The maximum speed of the particle will be:
  373. Depict the shown v-x graph in a-x graph
  374. A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point
  375. It takes one minute for a person standing on an escalator to reach the top from the ground. If the escalator is not moving, it takes him 3 minute to walk on the steps to reach the top. How long will it take for the person to reach the top if he walks up the escalator while it is moving?
  376. When a motorcycle moving with a uniform speed 11 m/s is at a distance 24 m from a car, the car starts from rest and moves with a uniform acceleration 2 m/s 2 away from the motorcycle. If the car begins motion at t: 0, time at which the motorcycle will overtake the car is t = 0, after the car is overtaken by the motorcycle, it will again overtake the motorcycle at what time, from t = 0 ?
  377. Trains A and B are moving towards each other on the same track with velocities 40 km/hr and 20 km/hr respectively. A sparrow which can fly at 30 km/hr flies off from train A when the trains are 30 km apart. The sparrow directly moves towards the train ‘B’ and on reaching there flies back to ‘A’ and so on. Distance travelled by the sparrow till the two trains will hit, is:
  378. Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed ‘a’ along the track so that the relative velocities of the trains with respect to the wind are in the ratio 1 :2, then the speed of each train must be:
  379. A bus is moving with a speed of 10 m s -1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of I km from the scooterist, with what speed should the scooterist chase the bus :
  380. Two particles P and Q start from rest and move for equal time on a straight line. Particle P has an acceleration of 2 m/s 2 for the first half of the total time and 4 m/s 2 for the second half. The particle Q has an acceleration of 4 m/ s 2 for the first half of the total time and 2m/s 2 for the second half. Which particle has travelled larger distance?
  381. A ball is thrown vertically upwards with some speed. It reaches two points A and B one after another such that heights of A and B are one fourth and three-fourth of the maximum height attained. If the total time of flight is T, the maximum time taken by the ball to travel from A to B, is :
  382. A car leaves Kota for Bundi every 12 minutes. The distance between Kota and Bundi is 60 km. The car travels at a speed of 60 km/hr. Find the number of cars that a man driving from Bundi to Kota will meet in route if he starts from Bundi simultaneously with one of the cars leaving Kota. The car from Bundi travels at a speed of 60 km/hr.
  383. Among the four graphs, there is only one graph for which average velocity over the time interval (0,T)can vanish for a suitable chosen T. Which one is it?
  384. Average velocity of the particle in time t=0 to t = 5 s is
  385. A stone is dropped from the top of a tower of height h. After 1 s another stone is dropped from the balcony 20 m below the top. Both reach the bottom simultaneously. What is the value of h ? Take g = 10 ms -2 .
  386. The relation between time t and distance x is x is t = ax 2 + βx where α and β are constants The retardation is
  387. For motion of an object along the x-axis, the velocity v depends on the displacement x as v = 3x 2 – 2x, then what is the acceleration at x = 2 m.
  388. A stone is dropped from the 25th storey of a multistoried building and it reaches the ground in 5 s. In the first second, it passes through how many storeys of the building? (g = 10 ms- 2 )
  389. A policeparty is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motorcycle. When he is at a distance x from the jeep, he accelerates from rest at a constant rate. Which of the following relations is true if the police is able to catch the dacoit?
  390. The average velocity of a body moving with uniform acceleration after travelling a distance of 3.06 m is 0.34 ms -1 . If the change in velocity of the body is 0.18 ms -1 during this time, its uniform acceleration is
  391. A point moves in a straight line so that its displacement x metre at time t second is given by x 2 = 1 + t 2 . Its acceleration in ms -2 at time t second is
  392. A point moves with uniform acceleration and v 1 , v 2 , and v 3 denote the average velocities in the three successive intervals of time t 1 , t 2 a n d t 3 . Which of the following relations is correct ?
  393. The velocity of a body moving in a straight line is given by V = (3x 2 + x)m/s. Find acceleration at x = 2m.
  394. A body has an initial velocity of 3 ms -1 and has an acceleration of 1 ms -1 normal to the direction of the initial velocity. Then its velocity 4 s after the start is
  395. A boy walks to his school at a distance of 6 km with constant speed of 2.5 kmh -1 and walks back with a constant speed of 4 kmh -1 . His average speed for round trip expressed (in kmh -1 ), is
  396. A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 kmh – 1 . Finding the market closed, he instantly turns and walks back home with a speed of 7 . 5 kmh – 1 . The average speed of the man over the interval of time 0 to 50 min is equal to
  397. The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point
  398. Figure given shows the distance-time graph of the motion of a car. It follows from the graph that the car is
  399. The velocity of a body depends on time according to the equation v = t 2 10 + 20 . The body is undergoing
  400. Particle A is moving along X-axis. At time t = 0, it has velocity of 10 ms – 1 and acceleration – 4 ms – 2 . Particle B has velocity of 20 ms – 1 and acceleration – 2 ms – 2 . Initially both the particles are at origin. At time t = 2 s, distance between the two particles is
  401. The displacement of a body along X-axis depends on time as x = t + 1 . Then, the velocity of body
  402. A body starts from rest with uniform acceleration a. The acceleration of the body as function of time t is given by the equation a = pt, where p is a constant, then the displacement of the particle in the time interval t = 0 to t = t 1 will be
  403. A particle moves along a straight line OX. At a time t (in seconds), the distance . x = 40 + 12 t – t 3 Then the displacement of the particle before coming to rest is
  404. A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. Then, which amongst the following option is correct about the relation between the distance covered by the boggy and distance covered by the train in the same time?
  405. A body moves for a total of nine second starting from rest with uniform acceleration and then with uniform retardation, which is twice the value of acceleration and then stops. The duration of uniform acceleration is
  406. A stone is allowed to fall freely from rest. The ratio of the time taken to fall through the first metre and the second metre distance is
  407. A particle moves a distance x in time t according to equation x = ( t + 5 ) – 1 . The acceleration of particle is proportional to
  408. Two particles P and Q simultaneously start moving from point A with velocities 15 ms – 1 and 20 ms – 1 respectively. The two particles move with accelerations equal in magnitude but opposite in direction. When P overtakes Q at B, then its velocity is 30 ms – 1 . The velocity of Q at point B will be
  409. The vertical height of point P above the ground is twice that of Q. A particle is projected downward with a speed of 5 ms – 1 from P and at the same time, another particle is projected upward with the same speed from Q. Both particles reach the ground simultaneously, then
  410. The given graph shows the variation of velocity with displacement. Which one of the graphs given below correctly represents the variation of acceleration with displacement?
  411. A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?
  412. Two cars A and B are travelling in the same direction with velocities v 1 and v 2 (v 1 > v 2 ). When the car A is at a distance d ahead of the car B, the. driver of the car A applied the brake producing a uniform retardation a. There will be no collision when
  413. A body is thrown vertically up with a velocity u. It passes three points A, Band e in its upward journey with velocities u 2 , u 3 and u 4 , respectively. The ratio of the separations between points A and B and between B and C, i.e. AB BC is
  414. Directions:These questions consists of two statements each printed as Assertion and Reason. While answering these questions you are required to choose anyone of the following four responses. Assertion :The v- t graph perpendicular to time axis is not possible in practice. Reason: Infinite acceleration cannot be realised in practice.
  415. Velocity and acceleration of a particle at some instant of time are v = ( 3 i ^ + 4 j ^ ) ms – 1 and a = – ( 6 i ^ + 8 j ^ ) ms – 2 , respectively. At the same instant particle is at origin, maximum x -coordinate of particle will be
  416. I. In the v-t diagram as shown in figure, average velocity between the interval t = 0 and t = t 0 is independent of t 0 . II. Average velocity in the given interval is 1 2 v m . Which amongst the statement(s) is/are correct?
  417. If a train travelling at 72 kmph is to be brought to rest in a distance of 200 metres, then its retardation should be
  418. Velocity of a body moving along a straight line with uniform acceleration (a) reduces by 3 4 of its initial velocity in time t o . The total time of motion of the body till its velocity becomes zero is
  419. A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30 m. Which of the following statements about the motion of the particle is false
  420. Let us call a motion, A when velocity is positive and increasing, A – 1 , when velocity is negative and increasing. R when velocity is positive and decreasing and R – 1 when velocity is negative and decreasing. Now, match the following two columns for the given s-t graph and mark the correct option from the codes given below. Column I Column II (A) M (p) A – 1 (B) N (q) R – 1 (C) P (r) A (D) Q (s) R Codes A B C D
  421. A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is (Take, g = 10 m / s 2 ) [NEET 2020]
  422. The initial velocity of a particle is u (at t = 0 ) and the acceleration f is given by at. Which of the following relation is valid
  423. The velocity of a body moving with a uniform acceleration of 2 m / sec 2 is 10 m / sec . Its velocity after an interval of 4 sec is
  424. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
  425. A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec each. Its initial velocity is
  426. A particle moves along a straight line such that its displacement at any time t is given by s = t 3 −   3 t 2   +    2 m The displacement when the acceleration becomes zero is
  427. A driver applies the brakes on seeing traffic signal 400 m ahead. At the time of applying the brakes vehicle was moving with 15 ms -1 and retarding with 0.3 ms -2 . The distance of vehicle after 1 minute from the traffic light is
  428. A body moves from rest with a constant acceleration of 5m/s 2 . Its instantaneous speed (in m/s) at the end of 10 sec is
  429. A body starting from rest, moves with uniform acceleration. The distance covered by the body in time t is proportional to
  430. Speed of a particle at 3rd and 8th second are 20 ms – 1 and zero respectively, then average acceleration between 3rd and 8th second will be [JIPMER 2019]
  431. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force q E, its velocity increases from 0 to 6 ms – 1 in one second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 s are respectively
  432. The displacement of a particle is given by y = a + bt + ct 2 − dt 4 . The initial velocity is
  433. The acceleration ‘a’ in m/s 2 of a particle is given by a = 3 t 2 + 2 t + 2 where t is the time. If the particle starts out with a velocity u = 2m/s at, t = 0 then the velocity at the end of 2 second is
  434. A particle starts from rest accelerates at 2 m/s 2 for 10s and then decelerates for 5s at 4 m/s 2 till it stops. What is the distance traveled by it
  435. A man moves from home to market which is at a distance of 2 km with a speed of 3 kmph. Finding the market closed he instantly returns home with a speed 6 kmph. The average velocity of the man in the total journey is
  436. The position x of a particle varies with time t as x = at 2 − bt 3 .The acceleration of the particle will be zero at time t equal to
  437. The velocity of a body depends on time according to the equation v = 20 + 0 .1 t 2 . The body is undergoing
  438. Velocity of a particle moving with constant acceleration changes from 20 ms -1 to 30 ms -1 in 5 seconds. Displacement of the body in the above interval is
  439. If a train travelling at 72 kmph is to be brought to rest in a distance of 200 metres, then its retardation should be
  440. A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30 m. Which of the following statements about the motion of the particle is false
  441. A particle starts from rest accelerates at 2 m/s 2 for 10s and then decelerates for 5s at 4 m/s 2 till it stops. What is the distance travelled by it
  442. A body starting from rest, moves with uniform acceleration. The distance covered by the body in time t is proportional to
  443. The distance travelled by a particle is directly proportional to t 1/2 , where t = time elapsed. What is the nature of motion ?
  444. A bullet fired into a target loses half of its velocity after penetrating 36 cm. Further distance covered by it before coming to rest will be
  445. A boy walks to his school at a distance of 6 km with constant speed of 2.5 km/h and walks back with a constant speed of 4 km/h. His average speed for the round trip is
  446. A driver applies the brakes on seeing traffic signal 400 m ahead. At the time of applying the brakes, vehicle was moving with 15 ms -1 and retarding with 0.3 ms -2 . The distance of vehicle after 1 minute from the traffic light is
  447. A tired man has moved through x metres in t minutes. If x = 80 t − 5 t 2 . What is the time elapsed and distance covered, before he comes to rest ?
  448. A particle starting with certain initial velocity and uniform acceleration covers a distance of 12 m in first 3 seconds and a distance of 30 m in next 3 seconds. The initial velocity of the particle is
  449. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is
  450. A particle located at x = 0, at time t = 0, starts moving along the positive X–direction with a velocity v that varies as v = α x . The displacement of the particle varies with time as
  451. A point moves in a straight line so that its displacement x m at time t sec is given by x 2    =    1 + t 2 . Its acceleration in m/sec2 at a time t sec is
  452. A train 200 m long crosses a bridge 300 m long. It enters the bridge with a speed of 30 ms -1 and leaves it with a speed of 50 ms -1 . What is the time taken to cross the bridge ?
  453. A bullet emerges from a barrel of length 1.2 m with a speed of 640 ms -1 . Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is
  454. A particle of unit mass undergoes one dimensional motion such that its velocity varies according to v ( x ) = β x – 2 n , where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by
  455. A ball is thrown upwards with a speed u from a height h above the ground. The time taken by the ball to hit the ground is
  456. The displacement of a particle as a function of time is shown in figure. It indicates that
  457. A vehicle moving with a constant acceleration from A to B in a straight line AB, has velocities u and v at A and B, respectively. C is the mid-point of AB. If time taken to travel from A to C is twice the time taken to travel from C to B, then the velocity of the vehicle v at B is
  458. A ball is projected upwards from the top of a tower with velocity 25 m s – 1 . If the height of the tower is 70 m, after what time from the instant of throwing, will the ball reach the ground? (Take, g = 10 m s – 2 )
  459. When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal, it can travel a distance x 1 along the plane. But when the inclination is decreased to 30° and the same object is shot with the same velocity, it can travel x 2 distance. Then, x 1 : x 2 will be
  460. The graph shown in figure shows the velocity v versus time t for a body. Which of the graphs shown in option represent the corresponding acceleration versus time graphs ?
  461. A balloon starts rising from the ground with an acceleration of 1.25 m/s 2 . After 8s, stone is released from the balloon. The stone will (Taking g = 10 ms –2 )
  462. A particle is projected vertically upwards from a point A on the ground. It takes time t 1 to reach a point B, but it still continues to move up. If it takes further t 2 time to reach the ground from point B, then height of point B from the ground is :
  463. Two balls are dropped from the same height at places A and B. The body at B takes two seconds less to reach the ground than the body at A and strikes the ground with a velocity greater than the body at A by 10 m/s. The product of the acceleration due to gravity at the two places A and B is ( in m 2 s –4 )
  464. A body thrown up vertically has a speed of 32 m/s, when it reaches half of the maximum height. It rises through a further height of ( g = 10 m/s 2 ) :
  465. A stone is projected up with a velocity of 98 m/sec. It reaches a point P in its path after 7 seconds. It reaches P again after another :
  466. A stone is dropped into a well and the sound of splash is heard after 5.33 sec. If the water is at a depth of 122.5 m from the ground, the velocity of sound in air is
  467. A stone is dropped from a height of 90cm above the top of a window which is 160 cm high. The time taken by the stone to cross the window is
  468. Water drops fall at regular intervals from a tap which is 5m above the ground. The third drop is leaving the tap at the instant, the first drop touches the ground. How far above the ground is the second drop at that instant ?
  469. Statement A : In the presence of heavy air resistance, the time of descent is longer than the time of ascent and the final speed will be smaller than the initial speed for a projected body. Statement B : During ascent the air resistance and gravity act in the same direction while during descent they act in the opposite direction.
  470. A balloon is rising steadily up with velocity of 19.6 m/s. If a stone is dropped from it, the separation between balloon and the stone after 2 seconds is
  471. An elevator ascends with an upward acceleration of 0.2m/ s 2 . At the instant its upward speed is 3m/ sec, a loose bolt 5m high from the floor of elevator drops from the celing of the elevator. Find the time untill the bolt strikes the floor
  472. A body falls from a height of 100 m. After 2 sec, if the gravity disappears, it strikes the ground after
  473. A ) When a body is projected up with a velocity ‘u’, it has zero velocity and non zero acceleration at the maximum height of its flight. B) The time taken to reach the maximum height and the time taken to reach the ground from maximum height for a body projected up are not equal if the air resistance is considered.
  474. The velocity of a body at an instant is 20 ms –1 . After 5s the velocity is 30 ms –1 . How many seconds earlier from the instant, it might have started? Assume acceleration is uniform
  475. Speeds of two cars are u and 4u at a specific instant. The ratio of respective distances in which two cars are stopped from that instant is(assuming they have same retardation)
  476. Average velocity of a particle moving in a straight line with constant acceleration ‘a’ and initial velocity ‘u’ in first ‘t’ second is
  477. A body is moving according to the equation x – at – bt 2 – ct 3 where x=displacement and a, b and c are constants. The acceleration of the body is
  478. A particle moving along a straight line has a velocity vms -1 , when it has cleared a distance y meter. These two are connected by the relation v = 49 + y . When its velocity is 1ms -1 , its acceleration(in ms -2 ) is
  479. A body covers 200 cm in the first 2 seconds and 220 cm in the next 4 seconds. The velocity of the body at the end of the 7 th second is
  480. The reaction time for an automobile driver is 0.7 sec. If the automobile can be decelerated at 5 m/s 2 , calculate the total distance travelled in coming to stop from an initial velocity of 8.33 m/s when a signal is observed.
  481. For motion of an object along the x-axis, the velocity ‘v’ depends on the displacement ‘x’ as v = 3x 2 – 2x, Then, what is the acceleration at x = 2m.
  482. The graph shown in figure shows the velocity v versus time t for a body. Which of the graphs shown in option represent the corresponding acceleration versus time graphs ?
  483. A balloon starts rising from the ground with an acceleration of 1.25 m/s 2 . After 8s, stone is released from the balloon. The stone will (Taking g = 10 ms –2 )
  484. Two balls are dropped from the same height at places A and B. The body at B takes two seconds less to reach the ground than the body at A and strikes the ground with a velocity greater than the body at A by 10 m/s. The product of the acceleration due to gravity at the two places A and B is ( in m 2 s –4 )
  485. A particle is projected vertically upwards from a point A on the ground. It takes time t 1 to reach a point B, but it still continues to move up. If it takes further t 2 time to reach the ground from point B, then height of point B from the ground is :
  486. A body thrown up vertically has a speed of 32 m/s, when it reaches half of the maximum height. It rises through a further height of ( g = 10 m/s 2 ) :
  487. A stone is projected up with a velocity of 98 m/sec. It reaches a point P in its path after 7 seconds. It reaches P again after another :
  488. A stone is projected vertically up at 40 m/sec. The time interval between two points at which the stone is 60 m above the ground is g = 10 m/sec 2 )
  489. A stone is dropped into a well and the sound of splash is heard after 5.33 sec. If the water is at a depth of 122.5 m from the ground, the velocity of sound in air is
  490. A stone is dropped from a height of 90cm above the top of a window which is 160 cm high. The time taken by the stone to cross the window is
  491. Water drops fall at regular intervals from a tap which is 5m above the ground. The third drop is leaving the tap at the instant, the first drop touches the ground. How far above the ground is the second drop at that instant ?
  492. A body falls on a planet through 9, 15, 21, 27 metres in successive seconds. The acceleration due to gravity on the planet is
  493. A body starts from rest and falls vertically from a height of 19.6 metre. If g = 9.8 ms -2 , then the distance travelled by the body in the last 0.1 seconds of its motion is
  494. Two balls of the same mass are shot upwards one after another at an interval of 2 seconds, along the same vertical line with the same initial velocity of 39.2 m/s. They will collide at a height :
  495. A ) When a body is projected up with a velocity ‘u’, it has zero velocity and non zero acceleration at the maximum height of its flight. B) The time taken to reach the maximum height and the time taken to reach the ground from maximum height for a body projected up are not equal if the air resistance is considered.
  496. The velocity of a body at an instant is 20 ms –1 . After 5s the velocity is 30 ms –1 . How many seconds earlier from the instant, it might have started? Assume acceleration is uniform
  497. A stone is dropped from the top of a multistoryed building. If it crosses 2 floors in the first second of its free fall, the number of floors it can cross in 4th second of its fall is
  498. A balloon is rising steadily up with velocity of 19.6 m/s. If a stone is dropped from it, the separation between balloon and the stone after 2 seconds is
  499. An elevator ascends with an upward acceleration of 0.2m/ s 2 . At the instant its upward speed is 3m/ sec, a loose bolt 5m high from the floor of elevator drops from the celing of the elevator. Find the time untill the bolt strikes the floor
  500. Statement A : In the presence of heavy air resistance, the time of descent is longer than the time of ascent and the final speed will be smaller than the initial speed for a projected body. Statement B : During ascent the air resistance and gravity act in the same direction while during descent they act in the opposite direction.
  501. For a particle in one dimensional motion, choose the correct option. a) For zero speed at an instant, it may have nonzero acceleration at that instant b) Particle having zero speed may have non zero velocity
  502. Speeds of two cars of same mass acted by same resistance force are u and 4u at a specific instant. The ratio of respective distances in which two cars are stopped from that instant is
  503. A body falls from a height of 100 m. After 2 sec, if the gravity disappears, it strikes the ground after
  504. A particle moving along a straight line has a velocity vms -1 , when it has cleared a distance y meter. These two are connected by the relation v = 49 + y . When its velocity is 1ms -1 , its acceleration(in ms -2 ) is
  505. A body is moving according to the equation x – at – bt 2 – ct 3 where x=displacement and a, b and c are constants. The acceleration of the body is
  506. The reaction time for an automobile driver is 0.7 sec. If the automobile can be decelerated at 5 m/s 2 , calculate the total distance travelled in coming to stop from an initial velocity of 8.33 m/s when a signal is observed.
  507. A body travels a distance of 20m in the 7 th second and 24 m in 9 th second. How much distance shall it travel in the 15 th second?
  508. A body covers 200 cm in the first 2 seconds and 220 cm in the next 4 seconds. The velocity of the body at the end of the 7 th second is
  509. Average velocity of a particle moving in a straight line with constant acceleration ‘a’ and initial velocity ‘u’ in first ‘t’ second is
  510. For motion of an object along the x-axis, the velocity ‘v’ depends on the displacement ‘x’ as v = 3x 2 – 2x, Then, what is the acceleration at x = 2m.
  511. A ball is thrown vertically upwards with a speed of 10 m/s and another ball is thrown vertically downwards with the same speed simultaneously. The time difference between them in reaching the ground )(in s) is: g = 10 m / s 2
  512. Two bodies of different masses m a   a n d   m b are dropped from two different heights, viz; a and b. the ratio of time taken by the two to drop through these distances, is:
  513. A parachutist after bailing out falls 50m without friction. When parachute opens, it decelerates at 2 m/ s 2 . He reaches the ground with a speed of 3m/s. At what height, did he bail out?
  514. A point initially at rest moves along x-axis. Its acceleration varies with time as a = 6 t + 5 m / s 2 . If it starts from origin, the distance covered in 2s is:
  515. A car accelerates from rest at a constant rate ‘ α ’ for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t, maximum velocity reached by the car is:
  516. The distance x travelled by a particle in time, t, is given by t = 2 x 2 + 3 x . If ‘u’ is the velocity, then acceleration will be:
  517. In 1.0 s, a particle goes from point A to B, moving in a semicircle of radius 1.0m. The magnitude of the average speed is:
  518. If a ball is thrown vertically upwards with speed u, the distance covered during the last ‘t’ seconds of its ascent is:
  519. Tripling the speed of a motor car multiplies the distance needed for stopping it by:
  520. From the top of tower, a stone is thrown up. It reaches the ground in t 1 second. A second stone thrown down with the same speed reaches the ground in t 2 second. A third stone released from rest reaches the ground in t 3 second. Then:
  521. A ball is thrown vertically upwards with a speed of 10 m/s and vertically downwards with the same speed simultaneously. The time difference between them in reaching the ground )(in s) is: g = 10 m / s 2
  522. Galileo’s experiment showed that if two bodies of unequal masses are dropped from the same height, the times required by them to reach the ground are equal. But if they are thrown the ratio of times required to reach the ground is equal to:
  523. Two bodies of different masses are dropped from two different heights, viz; a and b. the ratio of time taken by the two to drop through these distances, is:
  524. A body is projected vertically up from the ground. Taking air resistance into account, if t 1 is the time taken in going up while t 2 in coming down to starting point, then:
  525. A point initially at rest moves along x-axis. Its acceleration varies with time as a = 6 t + 5 m / s 2 . If it starts from origin, the distance covered in 2s is:
  526. A parachutist after bailing out falls 50m without friction. When parachute opens, it decelerates at 2 m/s 2 . He reaches the ground with a speed of 3m/s. at what height, did he bail out?
  527. The distance x travelled by a particle in time, t, is given by t = 2 x 2 + 3 x . If ‘u’ is the velocity, then acceleration will be:
  528. If a ball is thrown vertically upwards with speed u, the distance covered during the last ‘t’ seconds of its ascent is:
  529. 2 stones are thrown form top of tower, one vertically upward and other downward with same speed. Ratio of velocity when they hit the ground is:
  530. Tripling the speed of a motor car multiplies the distance needed for stopping it by:
  531. A particle moves a distance x in time t according to equation x = t + 5 − 1 . the acceleration of particle is proportional to:
  532. A car moves from X to Y with a uniform speed υ u and returns to Y with a uniform speed υ d . the average speed for this round trip is:
  533. The average velocity of a body moving with uniform acceleration travelling a distance of 3.06 m is 0.34 ms -1 . If the change in velocity of the body is 0.18 ms -1 during this time, its uniform acceleration is
  534. A car starts from rest and accelerates uniformly to a speed of 180 kmh- 1 in 10s. The distance covered by the car in the time interval is
  535. The velocity-time graph for two bodies A and B are shown in figure. Then, the acceleration of A and B are in the ratio
  536. A ball thrown vertically upwards after reaching a maximum height h returns to the starting point after a time of 10s. Its displacement after 5 s is
  537. A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the 4th second compared to that in the 3rd second is
  538. A car covers the first half of the distance between the two places at 40 kmh – 1 . and another half at 60 kmh – 1 . The average speed of the car is
  539. A particle starts moving from rest with uniform acceleration. It travels a distance x in first 2 s and distance y in the next 2 s. Then,
  540. A body starts from rest and moves with constant acceleration for t second. It travels a distance x 1 in first half of time and x 2 in next half of time, then
  541. The motion of a particle in straight line is an example of
  542. The velocity-time graph of particle comes out to be a non-linear curve. The motion is
  543. The velocity-time graph of robber’s car and a chasing police car are shown in the following graph. Police car crosses the robber’s car in time
  544. Initial speed of an α -particle inside a tube of length 4m is 1 kms – 1 . If it is accelerated in the tube and comes out with a speed of 9 kms – 1 , then the time for which the particle remains inside the tube is
  545. A particle moves along with X-axis. The position x of particle with respect to time t from origin is given by x = b 0 + b 1 t + b 2 t 2 . The acceleration of particle is
  546. A body X is projected upwards with a velocity of 98 ms – 1 , after 4 s, a second body Y is also projected upwards with the same initial velocity. Two bodies will meet after
  547. If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?
  548. A body of mass 2kg travels according to the relation x ( t ) = p t + q t 2 + r t 3 , where q = 4 ms – 2 , p = 3 ms – 1 and r = 5 m s – 3 . The force acting on the body at t = 2 s is
  549. A plot of Gibbs energy of a reaction mixture against the extent of the reaction is :
  550. The average velocity of a body moving with uniform acceleration travelling a distance of 3.06 m is 0.34 ms -1 . If the change in velocity of the body is 0.18 ms -1 during this time, its uniform acceleration is
  551. The motion of a particle along a straight line is described by equation x = 8 + 12 t – t 3 where, x is in meter and t in second. The retardation of the particle when its velocity becomes zero, is
  552. A body X is projected upwards with a velocity of 98 ms – 1 , after 4 s, a second body Y is also projected upwards with the same initial velocity. Two bodies will meet after
  553. Which of the following velocity (v) versus distance(s) graphs represent uniformly accelerated motion?
  554. The displacement of a particle moving in a straight line is described by the relation S = 6 + 12 t − 2 t 2 . Here S in meter and t is in sec. The distance covered by the particle in first 5s is
  555. A ball is thrown vertically upwards. Which of the following graphs represents speed – time graph of the ball during its flight (air resistance is neglected).
  556. A ball is thrown vertically upward with a velocity u from the top of a tower , it strikes the ground with velocity 3u. The time taken by the ball to reach the ground is
  557. Which of the following velocity (v) versus distance(s) graphs represent uniformly accelerated motion?
  558. A ball is thrown vertically upwards. Which of the following graphs represent speed – time graph of the ball during its flight (air resistance is neglected).
  559. Assertion (A) : A body is momentarily at rest at that instant it reverses the direction Reason (R) : A body can’t have acceleration if its velocity is zero at a given instant of time
  560. The acceleration – time graph of a particle moving in a straight line is shown in the fig. The velocity of the particle at time t=0 is 2ms -1 . The velocity after 2 seconds will be
  561. The acceleration – time graph of a particle moving in a straight line is shown in the fig. The velocity of the particle at time t = 0 is 2 ms − 1 . The velocity after 2 seconds will be
  562. A particle is moving along a straight line. For this motion you are given two statements A and B. Carefully examine them and select the correct option. Statement A: The velocity of the particle is always in the direction of its displacement Statement B: The acceleration of the particle is always in the direction of its velocity
  563. The velocity-time graph of a particle is shown in the diagram. Rank in order, from most positive to least positive, the accelerations at points A, B and C.
  564. A particle moves along the X-axis with its position x given as a function of time t by the equation x= -bt+ct 2 , where b and c are positive constants. At what time, the velocity of the particle will be equal in magnitude and opposite in direction to its initial velocity?
  565. A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t , then maximum velocity acquired by the car is given by
  566. A person travels along a straight road for the first half time with a velocity v 1 , and the second half time with a velocity v 2 . Then the mean velocity v is given by
  567. A passenger travels along the straight road for half the distance with velocity v 1 , and the remaining half distance with velocity v 2 . Then average velocity is given by
  568. A body starts from rest with uniform acceleration. If its velocity after n second is v, then its displacement in the last two seconds is
  569. A driver of an express train moving with a velocity v 1 finds that a goods train is moving with velocity v 2 in the same direction on the same track. He applies the brakes and produces a retardation a’ the minimum time required to avoid collision is
  570. Two cars are moving in the same direction with the same speed (= 30 km/h). They ale separated by a distance of b km. A truck moving in the opposite direction meets these two cars at an interval of 4 minute. The speed of truck is
  571. If displacement of a particle is zero, the distance covered
  572. If the distance covered is zero, the displacement:
  573. Position of particle moving along x-axis is given as x = (t-3) 2 , where x is in meter and t is in seconds. Distance covered by the particle in 6 seconds:
  574. A car moves from A to B with a speed of 30 km/h and from B to A with a speed of 20 km/h. What is the average speed of the car?
  575. Which of the following can be zero, when a particle is in motion for sometime?
  576. A particle travels one fourth of the distance constant speed of 5 m/s and remaining distance the constant speed of 18 m/s. What is the average speed of the car?
  577. The motion of a particle along a straight line is described by equation x = 8+12t-t 3 , where x is in metre and t is in second. The retardation of the particle when its velocity becomes zero, is:
  578. The velocity of a particle at an instant is 10 ms -1 . After 3 s its velocity will become 16 ms -1 . The velocity at 2 s, before the given instant would have been:
  579. A car moving with a speed of 50 kmh -1 can be stopped by brakes after atleast 6m. If the same car is moving at a speed of 100 kmh -1 , the minimum stopping distance is:
  580. The velocity of a particle is given by v = 180 – 16 x m / s . Its acceleration will be:
  581. The area under velocity-time graph for a particle in a given interval of time represents:
  582. The acceleration of a moving body is found from the:
  583. A body starting from rest moves along straight line with a constant acceleration. The variation of speed (v) with distance (s) is represented by the graph:
  584. A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight? (air resistance is neglected)
  585. Figure shows the position of a particle moving on the x-axis as a function of time. Choose the wrong statement.
  586. Which of the following cannot be the distance-time graph ?
  587. The graph of displacement-time for a body travelling in a straight line is given. We can conclude that:
  588. Two bodies, A (of mass 1kg) and B (of mass 3kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is:
  589. The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m, on the surface of A. What is the height of jump by the same person on the planet B?
  590. A stone is dropped from the top of a tower of height h. After 1s another stone is dropped from the balcony 20m below the top. Both reach the bottom simultaneously. What is the value of h? Take g=10 ms -2 .
  591. A car accelerates from rest at a constant rate for first 10s and covers a distance x. It covers a distance y in next 10s at the same acceleration. Then, which of the following is true?
  592. The velocity-time graph of a linear motion is shown below figure. The displacement from the origin after 8 seconds is
  593. The position of a point which moves in a straight line is given by x = bt 3 – ct where x is in metre, t in second and b and c are positive constants. when t = 2 second, the acceleration is 24 m/s 2 in positive x direction and at the same time, the velocity is 8 m/sec in negative x direction. Find the total time t required for the point to return to the origin at x = 0
  594. A point initially at rest moves along X-axis. Its acceleration varies with time as a = (6 t + 5) in m/s 2 . If it starts from origin, the distance covered in 1 sec is
  595. A passenger is at a distance x from a bus, when the bus begins to move with a constant acceleration a. What is the minimum velocity with which the passenger should run towards the bus so as to catch it ?
  596. A vechicle moving with a speed of 36 km/h sees a red light ahead dg applies brakes and stops after covering 10 m distances. If moving at a speed of 72 km/h then applying brakes it stops after covering 30 m distance. Assuming same reaction time and same deceleration in each case, the distance covered when brakes are applied on the vehicle when it is moving at 54 km/h is
  597. A frictionless wire is fixed between A and B inside a sphere of radius R. A small ball slips along the wire. The time taken by the ball to slip from A to B will be
  598. An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 2o m. If the car is going twice as fast, i.e., .120 km/h, the stopping distance will be
  599. The velocity of a particle is v = v 0 + gt +f t 2 .If its position is x = 0 at t = 0, then its displacement after unit time (t – 1) is
  600. A ball is dropped from a bridge 122.5 metres above a river. After the ball has been falling for two seconds, a second ball is thrown straight down after it. What must its initial velocity be so that both hit the water at the same time
  601. An object is projected upward with a velocity of 100 m/sec. It wilt strike the ground in approximately
  602. The distance travelled by a body falling from rest in the first, second and third seconds are in the ratio
  603. A boy throws a ball vertically upward in air in such a manner that when the ball is in its maximum height he throws another ball. If the balls are thrown after the time difference of 1, sec then what will be the height attained by them ?
  604. A stone is thrown upward with speed u attains maximum height h. Another stone thrown upwards from the same point with speed 2 u attains maximum height H. What is the relation between h and H
  605. A body dropped from the top of the tower covers a distance 7 h in the last second of its journey where h is the distance covered in the first second. How much time does it take to reach the ground ?
  606. A particle thrown up vertically reaches its highest point in time t 1 and returns to the ground in time t 2 . The air resistance exerts a constant force on the particle opposite to its direction of motion, then
  607. A boy sees a ball going up and then back down through a window 2.45 m high. If the total time taken by the ball is 1 sec, the height above the window that the ball rises is
  608. A train accelerates from rest for time t 1 at a constant rate α and then it retards at the constant rate β for time t 2 and come to rest. The ratio of t 1 /t 2 is equal to
  609. A body travels 200 cm in the first two second and 220 cm in the next 4 sec with deceleration. The velocity of the body at the end of the 7th second is
  610. A particle moves with an initial velocity v o and retardation α v, where v is its velocity at any time t. The velocity of the particle at time t = 1 / α will be
  611. The deceleration experienced by a .moving motor boat, after its engine is cut off is given by (dv / dt)= – K v 3 where K is a constant. If v o is the magnitude of the velocity at cut off, the magnitude of the velocity at a time t after the cut-off is
  612. A particle is moving in a straight line with constant acceleration. It crosses two points A and B with velocities α and β respectively. The velocity of particle at mid-point of line AB will be
  613. In 1 .0 s, a particle goes from point A to point B, moving in a semi-circle of radius 1.0 m see figure. The magnitude of average velocity is
  614. A car starts from rest, moves with an acceleration a and then decelerates at a constant rate b for some time to come to rest. It the total time taken is f, the maximum velocity of car is given by
  615. At the instant a motorbike starts from rest in a given direction, a car overtakes the bike, both moving in the same direction as shown in figure. The speed-time graphs for motor bike and car are represented by OAB and CD respectively. Then,
  616. Two boys are standing at the ends A and B of a ground where ,AB – a The boy at B starts running in a direction perpendicular to AB with velocity v 1 . The boy at A starts simultaneously with velocity y as shown in figure and catches the other boy in a time t, where t is
  617. The displacement x of a particle varies with time as x = ae − αt + be βt where e, b, o and F are positive constants. The velocity of the particle will
  618. The relation between time t and distance x is t=ax 2 +bx where a and b are constants. The acceleration is :
  619. A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known, On bouncing it rises to 1 .8 m. The ball loses its velocity on bouncing by a factor of
  620. A body is projected with a velocity u. It passes through a certain point above the ground after t 1 sec. The time after which the body passes through the same point during the return journey is
  621. A stone is dropped from a 25th storey of a multistoreyed building and it reaches the ground in 5 sec. In the first second, it passes through how many storeyed of the building ? (g = 10 m/s 2 )
  622. A body falls from a height h =200 m (at New Delhi). The ratio of distances travelled in each 2 sec during t = 0 to t = 6 sec of the journey is
  623. A ball is released from the top of a tower of height ft metre. It takes f second to reach the ground. What is the position of the ball in tl3 second ?
  624. A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one half of its maximum height. How high does the ball rise ? Tiake g = 10 m/s 2
  625. A juggler keeps on moving four balls in the air throws the balls in regular interval of time. When one ball leaves his hand (speed = 20 m/s), the positions of other balls will be (take g = 10 m/s 2 )
  626. Balls are thrown vertically upward in such a way that the next ball in thrown when the previous one is at the maximum height. If the maximum height is 5-m, the number of balls thrown per minute will be (take g =10 m/s 2 )
  627. A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time, the particle goes up is
  628. A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s 2 . He reaches the ground with a speed of 3 m/s. At what height, did he bail out ?
  629. The velocity of the particle 6 m/s eastwards changes to g m/s northwards in 10 s. what is the magnitude of the average acceleration during this interval of time?
  630. A person moves 3 m north and then zo m towards east and finally 30 2 m in south-west direction. The displacement of the person from the origin will be
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