A ball is thrown upwards with a speed of 40 m/s. When the speed becomes half of the initial speed, gravity is switched off for next 2 second. After that gravity is again switched on but magnitude of gravity is doubled. The total distance travelled by the ball from t = 0 to the time when the ball reaches the maximum height (in m) is Take g = 10 ms – 2
The velocity of an object moving rectilinearly is given as a function of time by v = 4t – 3t 2 , where v is in m/s and t is in seconds. The average velocity of particle between t = 0 to t = 2 seconds is
x -coordinate of a particle moving along this axis is x = 2 + t 2 + 2 t 3 . Here, x is in meters and t in seconds. Find the position from where it started its journey.
From the velocity-time plot shown in the given figure. Find the distance travelled by the particle during the first 40 s. Also find the average velocity during this period.
In one dimensional uniformly accelerated motion (acceleration =a ), find average velocity between from t = 0 t o t = t .
Give figure shows the graph of the x -coordinate of a particle going along x -axis as a function of time. Find the average velocity during 0 to 10 s.
Acceleration-time graph of a particle moving in a straight line is as shown in below figure. Velocity of particle at time t = 0 i s 2 m / s . Find the velocity at the end of fourth second.
A particle is thrown upwards with velocity u . Suppose it takes time t to reach its highest point, then distance travelled in last second is
A particle is moving along x -axis. Its x -coordinate versus time graph is as shown below. Plot v – t graph corresponding to this.
The body will speed up if
A particle moves in a straight line with the velocity as shown in figure. At t = 0, x = -16 m.
Average acceleration is in the direction of
Velocity versus displacement graph of a particle moving in a straight line is shown in figure. The corresponding acceleration versus velocity graph will be
A car accelerates from rest at a constant rate of 2 ms -2 for some time. Then it retards at a constant rate of 4 ms -2 and comes to rest. It remains in motion for 6 s.
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 m s -2 .
An object moves with constant acceleration a . Which of the following expressions is/are also constant?
The velocity-time graph of two bodies A and B is as shown in figure. Choose the correct statement.
A balloon rises from rest on the ground with constant acceleration 1.25 m s -2 . A stone is dropped when the balloon has risen to a height of 40 m. Find the time ( in sec) taken by the stone to reach the ground.
Two bodies 1 and 2 are projected simultaneously with velocities v 1 = 2 ms -1 and v 2 = 4 ms -1 respectively. The body 1 is projected vertically up from the top of a cliff of height h = 10 m and the body 2 is projected vertically up from the bottom of the cliff. If the bodies meet, find the time (in s) of meeting of the bodies.
A particle starts moving along a straight line path with a velocity 10 ms -1 . After 5 s, the distance of the particle from the starting point is 50 m. Which of the following statement about the nature of motion of the particle are correct?
A 200 m long train starts from rest at t = 0 with constant acceleration 4 cm s -2 . The head light of its engine is switched on at t = 60 s and its tail light is switched on at t = 120 s. Find the distance (in meter) between these two events for an observer standing on the platform.
Two cars start off to race with velocities 4 m/s and 2 m/s and travel in straight line with uniform accelerations 1 m/ s 2 a n d 2 m / s 2 r e s p e c t i v e l y . If they reach the final point at the same instant, then find the length of the path (in meter).
An elevator without a ceiling is ascending up with an acceleration of 5 m s -2 . A boy on the elevator shoots a ball in vertically upward direction from a height of 2 m above the floor of elevator. At this instant, the elevator is moving up with a velocity of 10 m s -1 and floor of the elevator is at a height of 50 m from the ground. The initial speed of the ball is 15 m s -1 w.r.t. the elevator. Consider the duration for which the ball strikes the floor of the elevator in answering following questions:
Two objects are moving along the same straight line. They cross a point A with an acceleration a a n d 2 a and velocity 2 u a n d u at time t = 0 . The distance moved by the object when one overtakes the other is
A rocket is fired vertically up from the ground with a resultant vertical acceleration of 10 m / s 2 . The fuel is finished in 1 min and it continues to move up. What is the maximum height reached?
At time t = 0 , a car moving along a straight line has a velocity of 16 ms – 1 . It slows down with an acceleration of – 0 . 5 t ms – 2 , where t is in second. Mark the correct statement (s).
Figure shows the velocity-time graph for a particle travelling along a straight line. The magnitude of average velocity (in m/s) of particle during the time interval from t = 0 to t = 6s is 10 α . Find the value of α .
A particle moves along the x-axis and its x-coordinate changes with time as x = u ( t − 2 ) + a ( t − 2 ) 2
Path of a particle moving in x-y plane is y = 3x + 4. At some instant suppose x-component of velocity is 1 m/s and it is increasing at a constant rate of 1 m/s 2 . Then, at this instant
A particle is moving in a straight line. Its retardation is given as a = − log e 2 V, here V is the speed of the particle in m/s. Find the time (in s) in which speed of the particle reduces to half.
A particle moves in positive x-direction according to law x = 12 t − t 2 m . where t time in second. (Take +ve x-axis as +ve). Based on the above facts, answer the following questions.
The motion of a particle along a straight line is described by the function x = ( 2 t – 3 ) 2 , where x is in meters and t is in seconds. Find the position, velocity and acceleration at t = 2 s .
A particle is moving with a velocity of v = 3 + 6 t + 9 t 2 cm / s . Find out the acceleration of the particle at t = 3 s .
A particle is moving with a velocity of v = 3 + 6 t + 9 t 2 cm / s . Find out the acceleration of the particle at t = 3 s .
Velocity and acceleration of a particle at time t = 0 are u = ( 2 i ^ + 3 j ^ ) m / s and a = ( 4 i ^ + 2 j ^ ) m / s 2 respectively. find the velocity and displacement of particle at t = 2 s .
x -coordinate of a particle moving along this axis is x = 2 + t 2 + 2 t 3 . Here, x is in meters and t in seconds. Find the position from where it started its journey.
x -coordinate of a particle moving along this axis is x = 2 + t 2 + 2 t 3 . Here, x is in meters and t in seconds. Find the position from where it started its journey.
The velocity of a particle moving in a straight line is directly proportional to 3 / 4 th power of time elapsed. How does its displacement and acceleration depends on time?
The motion of a particle along a straight line is described by the function x = ( 2 t – 3 ) 2 , where x is in meters and t is in seconds. Find the position, velocity and acceleration at t = 2 s .
Two particles A and B are moving along x -axis. Their x -coordinate versus time graphs are as shown below. (a) Find the time when the particles start …”> (a) Find the time when the particles start …”> (a) Find the time when the particles start …”> Find the velocities of the two particles.
Give figure shows the graph of the x -coordinate of a particle going along x -axis as a function of time. Find the average velocity during 0 to 10 s.
Corresponding to given v – s graph of a particle moving in a straight line, plot a – s graph.
The acceleration versus time graph of a particle is shown in figure. The respective v-t graph of the particle is
The acceleration-time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial velocity?
If acceleration is constant and initial velocity of the body is 0, then choose the correct statement. Symbols have their usual meaning.
From a lift moving upwards with a uniform acceleration a = 2 ms -2 , a man throws a ball vertically upwards with a velocity v = 12 ms -1 relative to the lift. The ball comes back to the man after a time t. Find the value of t in seconds. Take g = 10 m s – 2
Acceleration of particle moving rectilinearly is a = 4 – 2x (where x is position in metre and a in m s -2 ). It is at instantaneous rest at x = 0. At what position x (in meter) will the particle again come to instantaneous rest?
A body is allowed to fall from a height of 100 m. If the time taken for the first 50 m is t 1 and for the remaining 50 m is t 2 .
A thief is running away on a straight road in a jeep moving with a speed of 9 ms – 1 . A policeman chases him on a motor cycle moving at a speed of 10 ms – 1 . If the instantaneous separation of the jeep from the motor cycle is 100 m, how long will it take for the policeman to catch the thief?
A body is projected upwards with a velocity u. It passes through a certain point above the ground after time t 1 . The time after which the body passes through the same point during the return journey is
A train starts from station A with uniform acceleration a 1 for some distance and then goes with uniform retardation a 2 for some more distance to come to rest at station B. The distance between stations A and B is 4 km and the train takes 1/15 h to complete this journey. If accelerations are in km per sq. minute unit, then 1 a 1 + 1 a 2 = x . Find the value of x.
For a particle moving along the x-axis, a scaled x-t graph is shown in figure. Mark the correct statement(s).
A particle is moving along a straight line whose velocity – displacement graph is shown in figure. What is the retardation when displacement is 3 m?
The acceleration of a particle which moves along the positive x-axis varies with its position as shown in figure. If the velocity of the particle is 0.8 ms -1 at x = 0, then velocity of the particle at x = 1.4 m is (in ms -1 )
A particle is projected vertically upward with velocity u from a point A, when it returns to the point of projection
The displacement of a particle as a function of time is shown in figure. It indicates
A car is moving towards check post with velocity of 54 kmh -1 . When the car is at a distance of 400 m from the check post, the driver applies brakes which causes a deceleration of 0.3 ms -2 . Find the distance (in meter) of car from the check post for 2 minutes after applying the brakes.
Two trains are moving with velocities ? 1 = 10 ? ? – 1 a n d ? 2 = 20 ? ? – 1 on the same track in opposite directions. After the application of brakes if their retarding rates are a 1 = 2 m s – 2 a n d a 2 = 1 m s – 2 respectively, then the minimum distance of separation between the trains to avoid collision is
A thief in a stolen car passes through a police check post at his top speed of 90 kmh – 1 . A motorcycle cop, reacting after 2 s , accelerates from rest at 5 ms – 2 . His top speed being 108 kmh – 1 . Find the maximum separation between policemen and thief.
Two identical balls are shot upward one after another at an interval of 2 s along the same vertical line with same initial velocity of 40 m s – 1 . The height at which the balls collide is
A lift performs the first part of its ascent with uniform acceleration a and the remaining with uniform retardation 2 a . If t is the time of ascent, find the depth of the shaft.
A body starts from rest with uniform acceleration a , its velocity after n seconds is v . The displacement of the body in last 3 s is (assume total time of journey from 0 t o n second)
A body is thrown vertically upwards from the top A of tower. It reaches the ground in t 1 s . If it is thrown vertically downwards from A with the same speed it reaches the ground in t 2 s . If it is allowed to fall freely from A , then the time it takes to reach the ground is given by
Two particles A a n d B start from rest and move for equal time on a straight line. Particle A 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 B has acceleration 4 m / s ² for the first half and 2 m / s ² for the second half. Which particle has covered larger distance?
A car is travelling on a straight road. The maximum velocity the car can attain is 24 ms – 1 . The maximum acceleration and deceleration it can attain are 1 ms – 2 and 4 ms – 2 respectively. The shortest time the car takes from rest to rest in a distance of 200 m is,
A car is travelling on a road. The maximum velocity the car can attain is 24 ms – 1 and the maximum deceleration is 4 ms – 2 . If car starts from rest and comes to rest after travelling 1032 m in the shortest time of 56 s , the maximum acceleration that the car can attain is
Two points move in the same straight line starting at the same moment from the same point in it. The first moves with constant velocity u and the second from rest with constant acceleration f . Before the second catches the first , the greatest distance between the particle is
A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is 4 cm and that of iron plate is 2 cm . A bullet fired goes through the wood first and then penetrates 1 cm into iron. A similar bullet fired with the same velocity from opposite direction goes through iron first and then penetrates 2 cm into wood. If a 1 and a 2 be the retardations offered to the bullet by wood and iron plates respectively, then
The vertical height of point P above the ground is twice that of Q . A particle is projected downward with a speed of 5 m / s 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
A body is projected vertically upwards. If t 1 and t 2 be the times at which it is at height h above the point of projection while ascending and descending respectively, then h is
Speed-time graph of two cars A and B approaching towards each other is shown in figure. Initial distance between them is 60 m . The two cars will cross each other after time
A particle of mass m is initially situated at point P inside a hemispherical surface of radius r as shown in the figure. A horizontal acceleration of magnitude a 0 is suddenly produced on the particle in the horizontal direction. If gravitational acceleration is neglected, then time taken by the particle to touch the sphere gain is
Two particles P and Q simultaneously start moving from point A with velocities 15 m / s and 20 m / s , respectively. The two particles move with accelerations equal in magnitude but opposite in direction. At some instant velocity of P is 30 m / s . The velocity of Q at this instant
A ball is thrown vertically upwards with a speed $u$. It reaches a point B at a height h (lower than the maximum height) after time t 1 . It returns to the ground after time t 2 from the instant it was at B during the upward journey. Then, t 1 t 2 is equal to
A body is at rest at x = 0 . At t = 0 , it starts moving in the positive X -direction with a constant acceleration. At the same instant, another body passes through x = 0 moving in the positive X -direction with a constant speed. The position of the first body is given by x 1 ( t ) after time t and that of the second body by x 2 ( t ) after the same time interval. Which of the following graphs correctly describes x 2 – x 1 as a function of time?
From a tower of height H , a particle is thrown vertically upwards with a speed u . The time taken by the particle to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H , u and n is
A body starts with an initial velocity of 10 ms – 1 and is moving along a straight line with constant acceleration. When the velocity of the particle is 50 ms – 1 , the acceleration is reversed in direction. The velocity of the particle when it again reaches the starting point is
The acceleration-time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial speed?
Two stones are thrown up simultaneously with initial speeds of u 1 and u 2 u 2 > u 1 . They hit the ground after 6 s and 10 s respectively. Which graph in figure correctly represents the time variation of Δ x = x 2 – x 1 , the relative position of the second stone with respect to the first upto t = 10 s ? Assume that the stones do not rebound after hitting the ground.
A particle starting from rest and moving with a uniform acceleration along a straight line covers distances a and b in first p and next q second. The acceleration of the particle is
A rocket is fired vertically up from the ground with a resultant vertical acceleration of 10 m / s 2 . The fuel is finished in 1 min and it continues to move up. What is the maximum height reached?
A particle starting from rest has a constant acceleration of 4 m / s 2 for 4 s . It then retards uniformly for next 8 s and comes to rest. Find during the motion of particle average acceleration?
Displacement-time graph of a particle moving in a straight line is as shown in figure. Find the sign of velocity in regions o a , a b , b c and c d .
A particle having a velocity u = u 0 at t = 0 is decelerated at the rate | a | = α v , where α is a positive constant.
Velocity-time graph of a particle moving in a straight line is shown in figure, In the time interval from t = 0 to t = 14 s , find average speed of the partcile? (a)”> (a)”> (a)”>
Acceleration-time graph of a particle moving in a straight line is as shown in figure. At tin t = 0 , velocity of the particle is zero, Find velocity of the particle at t = 14 s ?
Velocity of a particle moving along positive x -direction is v = ( 40 – 10 t ) . Here, t is in seconds At time t = 0 , the x -coordinate of particle is zero. Find the time when the particle is at a point ( – 60 m , 0 ) from origin.
For a moving particle, which of the following options may be correct?
Identify the correct graph representing the motion of a particle along a straight line with constant acceleration with zero initial velocity.
The figure shows the velocity ( v ) of a particle plotted against time ( t ) “> “> “>
The speed of a train increases at a constant rate α from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate β . The total distance travelled by the train is l . The time taken to complete the journey is t . Then,
A car is moving with uniform acceleration along a straight line between two stops X and Y . Its speed at X and Y are 2 ms – 1 and 14 ms – 1 , Then
A point mass starts moving in a straight line with constant acceleration. After time t 0 the acceleration changes its sign, remaining the same in magnitude. Determine the time T from the beginning of motion in which the point mass returns to the initial position.
In one dimensional motion position of a particle from a fixed point is (say P ) is + 2 m at time t = 0 and the particle is at P at t = 10 s . If velocity of particle is zero at t = 6 s , determine the constant acceleration a and velocity at t = 10 s .
A particle moves along a horizontal path, such that its velocity is given by v = 3 t 2 – 6 t m / s where t is the time in seconds. If it is initially located at the origin O , determine the distance travelled by the particle in time interval from t = 0 to t = 3 . 5 s and the particle’s average velocity and average speed during the same time interval.
A particle travels in a straight line, such that for a short time 2 s ≤ t ≤ 6 s , its motion is described by v = ( 4 / a ) m / s , where a is in m / s 2 . If v = 6 m / s when t = 2 s , determine the particle’s acceleration when t = 3 s .
Velocity-time graph of a particle moving in a straight line is shown in figure. At time t = 0 , displacement of the particle from mean position is 10 m . Find acceleration of particle i n m / s 2 at t = 1 s , 3 s and 9 s ?
Velocity-time graph of a particle moving in a straight line is shown in figure. At time t = 0 , displacement of the particle from mean position is 10 m . Find acceleration of particle i n m / s 2 at t = 1 s , 3 s and 9 s ?
x and y -coordinates of a particle moving in x – y plane are, x = 1 – 2 t + t 2 and y = 4 – 4 t + t 2 For the given situation match the following two columns: Column I Column II (a) y -component of velocity when it crosses the y -axis (p) + 2 SI unit (b) x -component of velocity when it crosses the x -axis (q) – 2 SI unit (c) Initial velocity of particle (r) + 4 SI units (d) Initial acceleration of particle (s) None of the above
Two particles 1 and 2 are thrown in the directions shown in figure simultaneously with velocities 5 m / s and 20 m / s . Initially, particle 1 is at height 20 m from the ground. Taking upwards as the positive direction, find the acceleration of 1 with respect to 2?
The displacement ( x ) of a particle depends on time t as x = α t 2 – β t 3 . Choose the incorrect statements from the following.
A rocket is fired vertically up from the ground with a resultant acceleration of 10 m / s 2 , The fuel is finished in 1 min and it continues to move up g = 10 m / s 2
Two particles P and Q are moving along x -axis. Their position-time graph is shown in the figure Choose the correct options
An elevator without a ceiling is ascending up with an acceleration of 5 ms – 2 A boy on the elevator shoots a ball in vertical upward direction from a height of 2 m above the floor of elevator. At this instant the elevator is moving up with a velocity of 10 ms – 1 and floor of the elevator is at a height of 50 m from the ground. The initial speed of the ball is 15 ms – 1 with respect to the elevator. Consider the duration for which the ball strikes the floor of elevator in answering following questions. g = 10 m s – 2
A particle moves in a straight line with constant acceleration a . The displacements of particle from origin in times t 1 , t 2 and t 3 are s 1 , s 2 and s 3 respectively. If times are in AP with common difference d and displacements are in GP, then prove that a = s 1 – s 3 n d 2 .
At the initial moment three points A , B and C are on a horizontal straight line at equal distances from one another. Point A begins to move vertically upward with a constant velocity and point C vertically downward without any initial velocity but with a constant acceleration a . How should point B move vertically for all the three points to be constantly on one straight line. The points begin to move simultaneously.
An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2 . 2 m / s 2 and automobile has an acceleration of 3 . 5 m / s 2 . The automobile overtakes the truck when it (truck) has moved 60 m . How far was the automobile behind the truck initially?
A train stopping at two stations 4 km apart takes 4 min on the journey from one of the station to the other. Assuming that it first accelerates with a uniform acceleration x and then that of uniform retardation y , then.
Corresponding to velocity-time graph in one dimensional motion of a particle as shown in } \ figure, match the following two columns. Column I Column II (a) Average velocity between zero second and 4 s (p) 10 SI units (b) Average acceleration between 1 s and 4 s (q) 2.5 SI units (c) Average speed between zero second and 6 s (r) 5 SI units (d) Rate of change of speed at } 4 s (s) None of the above
The acceleration of particle varies with time as shown. (a) Find an expression for velocity in terms of t. (b) Calculate the displacement of the …”> (a) Find an expression for velocity in terms of t. (b) Calculate the displacement of the …”> (a) Find an expression for velocity in terms of t. (b) Calculate the displacement of the …”> Calculate the displacement of the particle i n m in the interval from t = 2 s to t = 4 s . Assume that v = 0 at t = 0 .
A particle is moving along x -axis. Its x -coordinate varies with time as : x = – 20 + 5 t 2 For the given equation match the following two columns : Column I Column II (a) Particle will cross the origin at (p) zero second (b) At what time velocity and acceleration are equal (q) 1 s (c) At what time particle changes its direction of motion (r) 2 s (d) At what time velocity is zero (s) None of the above
The v – s graph describing the motion of a motorcycle is shown in figure. Determine the time needed for the motorcycle to reach the position s = 120 m . Given ln 5 = 1 . 6 .
The jet plane starts from rest at s = 0 and is subjected to the acceleration shown. Determine the speed of the plane when it has travelled 60 m .
A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is x 1 , next 10 s is x 2 and the last 10 s is x 3 . Then, x 1 : x 2 : x 3 is
A body is thrown up with a velocity 100 ms -1 . It travels 5 m in the last second of its upward journey. If the same body is thrown up with a velocity 200 ms -1 , how much distance (in metre) will it travel in the last second of its upward journey(g = 10 ms -2 )?
In quick succession, a large number of balls are thrown up vertically in such a way that the next ball is thrown up when the previous ball is at the maximum height. If the maximum height is 5 m, then find the number of the balls thrown up per second (g =10 ms -2 ).
A lift performs the first part of its ascent with uniform acceleration a and the remaining with uniform retardation 2a and stops. If t is the time of ascent, the depth of the shaft is at 2 n . Find value of n.
The acceleration-time graph of a particle moving along a straight line is as shown in figure. At what time (in second) the particle acquires its initial velocity?
