A particle projected vertically upwards attains a maximum height H. If the ratio of the time to attain a height h (h<H) to the time to attain height H is 1/3 then
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
Two balls are dropped from the top of a high tower with a time interval of t 0 second, where t 0 is smaller than the time taken by the first ball to reach the floor, which is perfectly inelastic. The distance S between the two balls, plotted against the time lapse / from the instant of dropping the second ball, is best represented by
The acceleration versus time graph of a particle is shown in figure. The respective v-t graph of the particle is
A train 100 m long travelling at 40 ms -1 starts overtaking another train 200 m long travelling at 30 ms -1 . The time taken by the first train to pass the second train completely is
An object is vertically thrown upwards. Then the displacement-time graph for the motion is as shown in
Figure shows the displacement-time graph. From this graph, we conclude that the body is
A body goes 3km north and 4km east. What will be the magnitude of the displacement from initial point?
A car covers the first half of the distance between two stations at a speed of 30 kmph and the others half at 60 kmph. Then its average speed is
The splash is heard 2.05S after the stone is dropped into a well of depth 19.6m The velocity of sound is g = 9.8 m / s 2
A body 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
A body moving with uniform acceleration of 6 m / s 2 travels a distance of 27m in the last second of its journey. If it starts from rest, then the total time of its journey is
A body is dropped from the top of the tower covers a distance 7h in the last second if its journey, where ‘h’ is the distance covered in the first second. How much time does it take to reach the ground?
A body is projected vertically up with a speed of 20m/s. The distance travelled by it in 2sec is g = 10 m / s 2
A body covers the given distance first half of the time with a speed 58 kmph and second half of the time with a speed 75 kmph. Then the average speed of the body is.
A freely falling body moves from A to B during 2sec and from B to C during 1sec. If AB=BC the distance between A&B is
A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m / s t o 20 m / s while passing through a distance 135m in ‘t’sec . The value of ‘t’ is…………
A body is allowed to fall from a height of 100m. After 2s if acceleration due to gravity vanishes the total time of its fall is g = 10 m / s 2 in sec
The displacement ‘x’ (in m) of a particle at the instant when its velocity ‘v’ is given by v = 9 x + 25 m / s . Find its acceleration.
A body is dropped freely from a height of 19.6m. Find the velocity with which it strikes the ground?
A body dropped from the top of a tower hits the ground after 4 s. How much time does it take to cover the first half of the distance from the top of the tower?
The speed of a motor launch with respect to the water is v = 5 ms -1 , the speed of stream u= 3 ms -1 . When the launch began travelled 3.6 km up stream, turned about and caught up with the float. How long is it before the launch reaches the float again? (Find answer in hour).
Particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity v that varies as v = a x . The displacement of the particle varies with time as
A ball is dropped from height h=100 m,from surface of planet . if In the last 1 2 s of its journey, it covers a distance of 19 m.Then acceleration due to gravity (in m s – 2 ) on that planet is ———–
The velocity v and time (t) graph of a body moving in a straight line motion as shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is :
On a highway, two buses A and B are running at the same velocity of magnitude 30 ms -1 . The brakes caused a deceleration of 30 7 ms − 2 in bus A and that of bus B is 3 ms -2 . In an emergency when driver of the front car applies brakes, immediately its rear light turns red and braking begins. In response, driver of the rear bus also applies brakes to avoid a collision with the front bus. Every driver takes 1 s to apply the brakes after he saw a need for it. If bus A ahead of bus B, then the minimum separation between the buses before driver of bus A applies the brake is x. If bus B is running ahead of bus A, then the minimum separation between the buses before the driver of bus B applies brake is x 2 . The value of x 1 3 x 2 is
Balls A and B are released from rest from roof of a building at t=0 and t=2 s, respectively. The ball A strikes with ground and comes back with same speed. After some time, both balls A and B meet with each other at a height of 55 m from the ground. If the height of building is 60n meter, then the value of n is
A stone is thrown vertically upward. When the stone is at point A, its distance from a certain point O is 6 5 (OA=6 5 ) and the component of velocity along OA is nonzero. When it is at point B(OB= 10 m), the velocity at B is zero. When it is at point C(OC=6 m), the component of velocity of the particle along OC is zero. If the velocity of projection of the stone is v 0 = 5 n ms -1 , then the value of n is
A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is
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
The velocity acquired by a body moving with uniform acceleration is 30 ms -1 in 2 s and 60 ms -1 in 4 s. The initial velocity is
A particle moves with uniform acceleration along a straight line AB. Its velocities at A and B are 2 m/s and 14 m/s, respectively. M is the mid-point of AB. The particle takes t 1 seconds to go from A to M and t 2 seconds to go from M to B. Then t 2 /t 1 is
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?
A man swimming downstream overcome a float at a point M. After travelling distance D he turned back and passed the float at a distance of D/2 from the point M, then the ratio of speed of swimmer with respect to still water to the speed of the river will be
From a high tower, at time t = 0, one stone is dropped from rest and simultaneously another stone is projected vertically up with an initial velocity. The graph of distance S between the two stones plotted against time t will be
An object is thrown up vertically. The velocity-time graph for the motion of the particle is
Each of the three graphs represents acceleration versus time for an object that already has a positive velocity at time t 1 . Which graphs show an object whose speed is increasing for the entire time interval between t 1 and t 2 ?
An aero plane moves 400m towards north, 1200m towards east and then 300m vertically upwards. Then its displacement from initial position is
A body moves along a circules track of radius ‘R’. It starts from one end of a diameter moves along the circular track and completes 1 1 2 revolutions. Then the displacement is
A body starting from rest moves with uniform acceleration. The distance covered by the body in time ‘t’ is proportional to …..
A car starts from rest and moves with uniform acceleration ‘a’. Then the distance covered by the car in 5 th sec is
A body is released from the top of a tower of height h takes time ‘t’ to reach the ground. After time ‘ t ‘ 2 , the height from the ground is…..
A body is dropped freely from the top of a tower of height of 39.2 m. The time of descent is………..
A bullet fired into a fixed target loses half of its velocity in penetrating 20cm. How much further (in cm) it will penetrate before coming to rest?
A Scooter is going towards east at 20m/s turn right through an angle of 90 o . If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is
In travelling a distance of 3 kilometre between points A and D, a car is driven at 100 kmh -1 from A to B for t second and at 60 kmh -1 from C to D for t second. If the brakes are applied for 4 second between B and C to give the car a uniform deceleration, the value of t is
Figure shows the graph of the x-coordinate of a particle going along the x-axis as function of time. The speed of particle at t = 12.5 s (in ms -1 ) is ………..
A body initially at rest moving along x-axis in such a way so that its acceleration displacement plot is as shown in figure. What will be the maximum velocity of particle in ms -1 .
The displacement-time graph of a moving particle is as shown in the figure. The instantaneous velocity of the particle is negative at the point
An object, moving with a speed of 6.25 m/s, is declerated at a rate given by, dv dt = − 2 .5 v where v is the instantaneous speed. The time taken by the object, to come to rest would be
A particle moving in a straight line covers half the distance with Speed V o .The other half of the distance is covered in two equal time intervals with speed V 1 and V 2 respectively. The average speed of the particle during this motion is
A body travels for 15sec starting from rest with a constant acceleration . If it travels distances x, y and z in the first 5 sec,second 5 sec and the next 5 sec respectively. The relation between x, y and z is
A car moving with a speed of 40km/h can be stopped by applying the brakes after at least 2m. If the same car is moving with a speed of 80km/h, what is the minimum stopping distance?
A 150m long train is moving with a uniform velocity of 45km/h. The time taken by the train to cross a bridge of length 850m is
From the top of the tower of height 400 m, a ball is dropped by a man, simultaneously from the base of the tower, another ball is thrown up with a velocity 50 m/s; at what distance will they meet from the base of the tower?
A student is standing at a distance of 50 metres from a bus. As soon as the bus begins its motion (starts moving away from student) with an acceleration of 1 ms -2 , the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road. the minimum value of u, so that the student is able to catch the bus is:
A particle is projected with velocity v 0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e., a= α x 2 . The distance at which the particle stops is
A drunkard is walking along a straight road. He takes five steps forward and three steps backward and so on. Each step is 1 m long and takes 1 s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit after
A particle is moving in a straight line. and passes through a point o with a velocity of 6 ms -1 .The particle moves with a constant retardation of 2ms -2 for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O?
A ball is released from the top of a tower of height h. It takes time T to reach the ground. What is the position of the ball (from ground) after time T/3?
A particle slides from rest from the topmost point of a vertical circle of radius r along a smooth chord making an angle θ with the vertical. The time of descent is
A body dropped from the top of a tower covers a distance 7x in the last second of its journey, where x is the distance covered in the first second. How much time does it take to reach the ground?
A bus is moving with a velocity 10 ms -1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus?
A particle is thrown up inside a stationary lift of sufficient height. The time off light is T. Now it is thrown again with same initial speed v 0 with respect to lift. At the time of second throw, lift is moving up with speed v 0 and uniform acceleration g upward (the acceleration due to gravity). The new time of flight is
The displacement-time graph of a moving particle with constant acceleration is shown in figure. The velocity-time graph is given by
An insect moving along a straight line, travels in every second distance equal to the magnitude of time elapsed. Assuming acceleration to be constant, and the insect starts at t = 0. Find the magnitude of initial velocity of insect
On a highway, two buses A and B are running at the same velocity of magnitude 30 ms -1 . The brakes cause a deceleration or A ms -2 in bus A and that of bus B is 30 7 ms − 2 . In an emergency when driver of the front car applies brakes, immediately its rear light turns red and braking begins. In response, driver of the rear bus also applies brakes to avoid a collision with the front bus. Every driver takes 1 s to apply the brakes after he saw a need for it. If bus A ahead of bus B, then the minimum separation between the buses before driver of bus I applies the brake is x 1 . If bus B is running ahead of bus A, then the minimum separation between the buses before the driver of bus B applies brake is x 2 . The value of x 1 3 x 2 is .
A lift performs the first part of ascent with uniform acceleration a and the remainder with uniform retardation 2a. The lift starts from rest and finally comes to rest. If t is the time of ascent. Find the height ascended by lift.
A truck is moving at a speed of 72 kmh -1 on a straight road. The driver can produce deceleration of 2 ms -2 by applying brakes. The stopping distance of truck is 13x m, if the reaction time of the driver is 0.2 s. The value of x is .
A stone is thrown vertically upward. When the stone is at point A, its distance from a certain point O is 6 5 m at t=0 and the component of velocity along OA is nonzero. When it is at point B(OB=10 m), the component of velocity along OB is zero. When it is at point C (OC=6 m), the component of velocity of the particle along OC is zero. If the velocity of projection of the stone is v 0 = 5 n ms -1 , then the value of n is .
A particle is thrown upwards from ground. It experiences a constant air resistance force which can produce a retardation of 2 m/s 2 . The ratio of time of ascent to the time of descent is
A train is moving on straight track with velocity v 0 = 13.5 ms -1 . To stop the train at a particular station, the driver applies brakes at t = 0, which is caused of a retardation proportional to the velocity of the train. The speed of train reduces 50% in the first 2 s in t 0 =4 . The velocity of train (in ms -1 ) at t=4s (Given , e=2.7)is
A fun drive in an amusement park runs between two spots that are 2.0 km apart. For safety reasons the acceleration of the drive is limited to ± 4.0 m/s 2 , and the jerk, or rate of change of acceleration, is limited to ± 1.0 m/s 2 . The drive has a maximum speed of 144 km/h. If the shortest time taken by the drive to travel between the spots is n 2 , The value of ‘n’ is .
A runner travels around a rectangular track of length 70m and width 30m. After travels around the rectangular track two times, runner back to starting point. Determine distance travelled by the runner.
Speedometer of an automobile measures:
A car is travelling on a straight line moves with a uniform velocity V 1 for a distance 20m and with a uniform velocity V 2 for the next equal distance. Then the average velocity ‘V’ is given by…
A body moving along a straight line changes its velocity from 20 m / s to 40 m / s in 5S . Find its acceleration:
A car starts from rest and moves along a straight road with a uniform acceleration of 12 m / s 2 . What is the distance travelled after a time of 6Sec from the start?
A point moves in a straight line so that its displacement ‘ y ‘ m at time ‘ t ‘ sec is given by y 2 = 1 + t 2 . Its acceleration in m / s 2 at time ‘ t ‘ sec
If x denotes displacement in time t and x=asint then acceleration is
A particle moving with a constant acceleration describes in the last second of its motion 9 25 t h of the whole distance. If it starts from rest, how long is the particle is motion.
A body is projected vertically upwards with a speed of 15m/s. Then the time of flight of the body is………. g = 10 m / s 2
A body falls freely from a height ‘h’, its average velocity when it reaches the earth is ………..
A body is projected vertically upwards with a velocity of 19.6m/s. Then the maximum height reached by the body…..
A stone is thrown vertically upward with a speed of 10m/s from the edge of a cliff 65m high. What will be its speed just before hitting the bottom?
Acceleration of a particle at any time t is a ¯ = 2 t i ^ + 3 t 2 j ^ m / s 2 . If initially particle is at rest find the velocity of the particle at time t=2 sec
A body is thrown vertically down wards from a height of 48m. It reaches the ground in 2s. Find the initial speed with which it was thrown?
A ball is dropped from a height ‘h’ and another from height 4h. The ratio of time taken by the two balls to reach ground is……..
A body falls from a height h=300m, the ratio of distances travelled in each 2s, during t=0 to t=6s in the journey is:…….
A body goes 10km north and 20km east what will be the magnitude of the displacement from initial point?
A body starts from rest and moves with a uniform acceleration of 20 m/s 2 in the first 10s. During the next 10s it moves with the maximum velocity attained uniformly. The total displacement of the body is
A particle has an initial velocity of 3 i ^ + 4 j ^ and an acceleration of 4 i ^ + 3 j ^ . Then its speed in 10s is…..
A ball is dropped from a height. Another ball is dropped from the same height after 4s. Their separation after 2 more seconds is ……….. m g = 9.8 m / s 2
A helicopter is ascending vertically with a speed of 8m/s. At a height of 120m above the earth, a stone is dropped from a window. How much time does it take for the stone to reach the ground.
A car, starting from rest, is accelerated at a constant rate α until it attains a speed ν . It is then retarded at a constant rate β until it comes to rest. The average speed of the car during its entire journey is
The velocity of a car travelling on a straight road is given by the equation v = 9 + 8 t – t 2 where v is in metre per second and t in second. The instantaneous acceleration when t = 5s is
A body is projected with kinetic energy K at an angle of 60° with the horizontal. Its kinetic energy at the highest point of its trajectory will be
A particle moving in a straight line covers half the distance with speed of 3 ms -1 . The other half of the distance is covered in two equal time intervals with a speeds of 4.5 ms -1 and 7.5 ms -1 respectively. Find the average speed (in m/s) of the particle during this motion
A stone falls from rest. The distance covered by the stone in the last second of its motion equals the distance covered by it during the first three seconds of its motion. How long (in seconds) does the stone take to reach the ground? Take g = 10 ms – 2
The displacement x of a particle moving in a straight line varies with time t as x 2 = a + bt 2 where a and b are constants. The acceleration of the particle at time t is given by
A body starts from rest and moves with a constant acceleration. The ratio of distance covered in the nth second to the distance covered in n second is
The ratio of the numerical values of the average velocity and the average speed of a body is always
A particle is moving in a straight line under constant acceleration. If the motion starts from rest, find the ratio of displacement in “n th” seconds to that in the n second
A car moving on a straight road covers one third of the total distance with a speed of 20 km/hr and the rest with a speed of 60 km/hr. The average speed is
Two particles A and B are at separation of 100 m, particle A moves with constant acceleration 4 m / s 2 with initial speed 5m/s and B moves with uniform speed 12m/s, towards each other. When and where the particles meet?
A body is moving with a uniform acceleration covers 40m in the first 4 sec and 120m in next 4 sec. Its initial velocity and acceleration are
A particle starts its motion from rest under the action of a constant force. If the distance covered in the first 10 sec is x and that covered in the first 20 sec is y then
A body moving with a uniform acceleration crosses a distance of 15m in the 3rd second and 23m in the 5th second. The displacement in 10sec will be
A bullet fired into a fixed target loses half of its velocity after penetrating through a distance 1 cm. How much further distance it will penetrate before coming to rest. (Assuming that it faces constant retardation)
A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m/s to 20 m/s while passing through a distance of 135 m in time of “t” second. Then value of time “t” is
Two cars A and B are at rest at the origin O. If A starts with a uniform velocity of 20 m/s and B starts in the same direction with a constant acceleration of 2m/ s 2 , then the cars will meet after time
Two trains travelling on the same track are approaching each other with an equal speed of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2 km apart. Assuming the deceleration to be uniform and equal , the value of the deceleration to barely avoid collision should be …..in m/ s 2
A cyclist starts from rest and moves with a constant acceleration of 1 m/ s 2 . A boy who is 48 m behind the cyclist starts moving with a constant velocity of 10 m/s. After how much time the boy meets the cyclist?
A man is” d” distance behind the bus. when the bus starts from rest with an acceleration a 0 , With what minimum constant velocity should the man start running to catch the bus
A body” A ” starts from rest with an acceleration a 1 . After 2 sec, another body” B ” starts from rest with an acceleration a 2 . If they cover equal distances in the 5th second after the start of A, then the ratio of a 1 : a 2 is equal to
A particle is moving with constant acceleration from A to B in a straight line AB. If U and V are the velocities of particle at A and B respectively, then its velocity of particle at the midpoint C will be
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 the maximum velocity attained is
A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of 2 g h . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of h g is :
The distance x covered by a particle in one dimensional motion varies with time t as x 2 = a t 2 + 2 b t + c . If the acceleration of the particle depends on x as x − n , where n is an integer, the value of n is
Train A and train B are running on parallel tracks in the opposite directions with speeds of 36km/hour and 72km/hour respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8km/hour. Speed (in m s – 1 ) of this person as observed from train B will be close to: (take the distance between the tracks as negligible)
A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height h 2 . The velocity versus height of the ball during its motion may be represented graphically by : (graph are drawn schematically and on not to scale)
The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be
The helicopter rises from rest on the ground vertically upwards with a constant acceleration g . A food packet is dropped from the helicopter when it is at a height h. Time taken by the packet to reach the ground is closed to [ g is the acceleration due to gravity]
A balloon is moving up in air vertically above a point A on the ground . When it is at high h 1 ,a girl standing at a distance d ( point B from A) (see figure) sees it at an angle 45 0 with respect to the vertical . When the balloon climbs up a further height h 2 , it is seen at an angle 60 0 with respect to the vertical if the girl moves further by a distance 2.464d (Point C) . Then the height h 2 is ( Given tan 30 0 =0.5774):
A particle moves from the point 2 i ^ + 4 j ^ m , at t=0 with an initial velocity 5 i ^ + 4 j ^ m / s . It is acted upon by a constant acceleration 4 i ^ + 4 j ^ m / s 2 . What is the distance of the particle from the origin at time t = 2 s in meters?
The velocity of a particle in a straight line motion is given by v = 10 − 10 t . The correct graphical representation of displacement -time graph of motion is ( s-displacement, t – time)
For the graph shown in the fig., find area under the velocity time graph from t = 0 to t = 12 second.
A police van moving on a high way with a speed of 30km/h fires a bullet at a thief’s car speeding away in the same direction with a speed of 192km/h. If the speed of the bullet with respect to police Van is 150m/s, with what relative speed does the bullet hit the thief’s car?
A truck is moving at a speed of 72 kmh -1 on a straight road. The driver can produce deceleration of 2 ms -2 by applying brakes. The stopping distance of truck is 13x m, if the reaction time of the driver is 0.2 s. The value of x is
On a city road, the last traffic light glows green for 60 s and red for 120 s. The range of speeds of vehicles is from 50 3 ms − 1 to 200 9 ms − 1 in a group. The speed of each vehicle is constant. It is found that at a distance x from traffic light, then the successive groups pushing through traffic light place will become indistinguishable. The value of x (in km) is
A stone thrown vertically upward from a certain height. It covers half of distance covered during the time of flight to last second. The time of flight (in second) of the stone is
A length of path ACB is 1500 m and the length of the path ADB is 2100 m. Two particles start from point A simultaneously around the track ACBDA. One of them travels the track in clockwise sense and other in anticlockwise sense with their respective constant speeds. After 12 s from the start, the first time they meet at the point B. After minimum time (in s) in which they meet first at point B, will they again meet at the point B is time t min = ( 12 ) x s . The value of x is
A particle starts from rest and moves with acceleration a which varies with time t as a=kt where k is a constant. The displacement s of the particle at time t is
If a body is projected vertically up, its velocity decrease to half of its initial velocity at a height ′h′ above the ground. Then maximum height reached by it is p h 3 . Find the value of p .
A thief is running away on a straight road in jeep moving with a speed of 9 ms -1 A police man chases him on a motor cycle moving at a speed of 10 ms -1 . If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police to catch the thief
Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their acceleration are 0.3 m/s 2 and 0.2 m/s 2 , respectively, then the time they take to pass each other will be
A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are
balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is
A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is
A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds, a second projectile is fired vertically upwards, also with initial velocity u.
A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is
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
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)
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 y varies with the height h above the ground is correctly shown in
A ball is thrown straight upward with a velocity v 0 from a height h above the ground. The time taken for the ball to strike the ground is
From the top of the tower of height 400 m, & ball is dropped by a man, simultaneously from the base of the tower, another ball is thrown up with a velocity 50 m/s; at what distance will they meet from the base of the tower?
The magnitude of displacement is equal to the distance covered in a given interval of time if the particle
The distance travelled by a particle in a straight line motion is directly proportional to t 1/2 , where t is the time elapsed. What is the nature of motion?
Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as function of time as the trains slow down. The separation between the trains when both have stopped is
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, where t is equal to
Between two stations, a train accelerates from rest uniformly at first, then moves with constant velocity, and finally retards uniformly to come to rest. If the ratio of the time taken is 1:8:1 and the maximum speed attained be 60 km h -1 , then what is the average speed over the whole journey?
A particle starts from the origin with a velocity of 10 m s -1 and moves with a constant acceleration till the velocity increases to 50 ms -1 . At that instant, the acceleration is suddenly reversed. What will be the velocity of the particle, when it returns to the starting point?
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?
The displacement x of a particle moving in one dimension under the action of a constant force is related to time t by the equation t = x + 3 , wherex is in meters and t is in seconds. Find the displacement of the particle when its velocity is zero.
The relation between time t and distance x is t = α x 2 + β x where α and β are constants. The retardation is
A body travels 200 cm in the first 2 s and 220 cm in the next 4 s with deceleration. The velocity of the body at the end of the seventh second is
A body starts from rest and travels a distance S with uniform acceleration, then moves uniformly a distance 2S uniformly, and finally comes to rest after moving further 5S under uniform retardation. The ratio of the average velocity to maximum velocity is
A police party 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?
A moving car possesses average velocities of 5 ms -1 , 10 ms -1 , and 15 ms -1 in the first, second, and third seconds, respectively. What is the total distance covered by the car in these 3 s?
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
A body is released from the top of a tower of height H m. After 2 s, it is stopped and then instantaneously released. What will be its height after next 2 s?
A stone is dropped from the top of a tower of height h. After I 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 .
A person is throwing two balls in the air one after the other. He throws the second ball when the first ball is at the highest point. If he is throwing the balls every second, how high do they rise?
A stone thrown upwards with speed u attains maximum height h. Another stone thrown upwards from the same point with speed 2u attains maximum height H. What is the relation between h and H?
The distances moved by a freely falling body (starting from rest) during 1st, 2nd ,3rd, . . ., n th second of its motion are proportional to
A stone is dropped from a certain height which can reach the ground in 5 s. It is stopped after 3 s of its fall and then it is again released. The total time taken by the stone to reach the ground will be
A body sliding on a smooth inclined plane requires 4 s to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth the distance starting from rest at the top?
B 1 , B 2 , and B 3 are three balloons ascending with velocities v, 2v, and 3v, respectively. If a bomb is dropped from each when they are at the same height, then
A ball is thrown from the top of a tower in vertically upward direction. The velocity at a point h meter below the point of projection is twice of the velocity at a point h meter above the point of projection. Find the maximum height reached by the ball above the top of tower.
A juggler keeps on moving four balls in air throwing the balls after regular intervals. When one ball leaves his hand (speed = 20 m s -1 ), the position of other balls (height in meter) will be (take g = 10 ms -2 )
A body is thrown vertically upwards from A, the top of a tower. It reaches the ground in time t 1 . lf it is thrown vertically downwards from A with the same speed, it reaches the ground in time t 2 . If it is allowed to fall freely from A, then the time it takes to reach the ground is given by
A body is projected upwards with a velocity u. It passes through a certain point above the ground after t 1 . The time after which the body passes through the same point during the return journey is
A paruchutist drops first freely from an aeroplane for 10 s and then his parachute opens out. Now he descends with a net retardation of 2.5 ms -2 . If he bails out of the plane at a height of 2495 m and g = 10 ms -2 , his velocity on reaching the ground will be
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
Water drops fall from a tap on the floor 5 m below at regular intervals of time, the first drop striking the floor when the fifth drop begins to fall. The height at which the third drop will be from ground (at the instant when the first drop strikes the ground) will be g = 10 ms − 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 m s -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 train is moving at a constant speed V when its driver observes another train in front of him on the same track and moving in the same direction with constant speed v. If the distance between the trains is x, then what should be the minimum retardation of the train so as to avoid collision?
A person A is sitting in one train while another person B is in the second train. The trains are moving with velocities 60 m/s and 40 m/s, respectively, in the same direction. Then the velocity of B relative to A will be
Imagine yourself standing in an elevator which is moving with an upward acceleration a = 2 m / s 2 .A coin is dropped from rest from the roof of the elevator, relative to you. The roof to floor height of the elevator is 1.5 m. (Take g = 10 m / s 2 ). rind the velocity of the coin relative to you when it strikes the base of the elevator.
It takes one minute for a passenger standing on an escalator to reach the top. If the escalator does not move it takes him 3 minute to walk up. How long will it take for the passenger to arrive at the top if he walks up the moving escalator?
A bird flies to and fro between two cars which move with velocities v 1 =20 m/s and v 2 =30 m/s. If the speed of the bird is v 3 =10 m/s and the initial distance of separation between them is d=2 km, find the total distance covered by the bird till the cars meet.
The variation of velocity of a particle moving along a straight line is shown in figure. The distance travelled by the particle in 12 s is
From the velocity-time graph, given in figure of a particle moving in a straight line, one can conclude that
The velocity-time graph of a body is given in figure. The maximum acceleration in ms -2 is
The following graph (figure) shows the variation of velocity of a rocket with time. Then the maximum height attained by the rocket 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?
Plot the acceleration-time graph of the velocity y a x i s -time x a x i s graph given in the figure.
Graph of ( 1/v) vs. x for a particle under motion is as shown, where v is velocity and x is position. The time taken by particle to move from x = 4 m to x = 12 m is
The drawing shows velocity (v) versus time (r) graphs for two cyclists moving along the same straight segment of a highway from the same point. The second cyclist starts moving at t = 3 min. At what time do the two cyclists meet?
train normally travels at a uniform speed of 72V,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 along 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?
Each of the four particles move along an x-axis. Their coordinates (in metres) as function of time (in seconds) are given by Particle 1: x ( t ) = 3.5 − 2.7 t 3 Particle 2 : x ( t ) = 3.5 + 2.7 t 3 Particle 3: x ( t ) = 3.5 + 2.7 t 2 Particle 4: x ( t ) = 3.5 − 3.4 t − 2.7 t 2 which of these particles is speeding up for t > 0?
When two bodies move uniformly towards each other, the distance between them diminishes by 16 m every 10 s. If bodies move with velocities of the same magnitude and in the same direction as before the distance between then will decrease 3 m every 5 s. The velocity of each body is.
Two objects moving along the same straight line are leaving point A with an acceleration a,2a and velocity 2u, u respectively at time t=0. The distance moved by the object with respect to point A when one object overtakes the other is
Two particles P and Q start from rest and move for equal time on a straight line. Particle P has an acceleration of X m/s 2 for the first half of the total time and 2X m/s 2 for the second half. The particle Q has an acceleration of 2X m/s 2 for the first half of the total time and Xm/s 2 for the second half. Which particle has covered larger distance?
A particle moving along a straight line with a constant acceleration of 4 m/s 2 passes through a point A on the line with a velocity of +8 m/s at some moment. Find the distance travelled by the particle in 5 seconds after that moment.
A particle starts from rest with uniform acceleration and its velocity after n seconds is v. The displacement of the body in last two seconds is
A stone is dropped from the top of a tower. When it has fallen by 5 m from the top, another stone is dropped from a point 25 m below the top. Ifboth stones reach the ground at the same moment, then height of the tower is (take g = 10 m/s 2 )
Two bikes A and B start from a point. A moves with uniform speed 40 m/s and B starts from rest with uniform acceleration 2 m/s 2 . lf B starts at t =10 and A starts from the same point at t = 10 s, then the time during the journey in which A was ahead of B is
On a city road, the last traffic light glows green for 60 s and red for 120 s. The range of speeds of vehicles is from 50 3 ms − 1 to 200 9 ms − 1 in a group. The speed of each vehicle is constant. It is found that at a distance x from traffic light, then the successive groups pushing through traffic light place will become indistinguishable. The value of x (in km) is .
A length of path ACB is 1500 m and the length of the path ADB is 2100 m. Two particles start from point A simultaneously around the track ACBDA. One of them travels the track in clockwise sense and other in anticlockwise sense with their respective constant speeds. After 12 s from the start, the first time they meet at the point B. After minimum time (in s) in which they meet first at point B, will they again meet at the point t min = ( 12 ) x s . The value of x is .
Balls A and B are released from rest from roof of a building at t = 0 and t = 2 s, respectively. The ball A strikes with ground and comes back with same speed. After some time, both balls A and B meet with each other at a height of 55 m from the ground. If the height of building is 60n metre, then the value of n is .
A ball is thrown vertically upward from the roof of a building with a certain velocity. It reaches the ground in 9 s. When it is thrown downward from the roof with the same initial speed, it takes 4 s to come at ground. How much time (in second) will it take to reach at ground if it just released from the rest from the roof?
A particle is moving on a straight line whose velocity as function of time is (t -2) ms -1 . The distance travelled by particle (in m) in 4 s is .
A ball is released from rest from top of a tower. The retardation due to air resistance is bv, where b is 10 per second and velocity v is ms -1 . The velocity of ball at t = 1 10 s is n 27 ms − 1 The value of n (Given, e=2.7) is .
The maximum acceleration or deceleration that a train may have is a = 5 ms -2 . The minimum time in which the train may reach from one station to the other separated by a distance d=500 m is t 0 =5 n s. The value of n is .
A particle is moving along X-axis. At instant to, instantaneous velocity is equal to average velocity from t = 0 to t = t 0 The value of t 0 is 16 n s The value of n is .
Two motorboats, which can move with velocities 4.0 m/s and 6.0 m/s relative to water are going up-stream. When the faster one overtakes the slower one, a buoy is dropped from the slower one. After lapse of sometime both the boats turn back simultaneously and move at the same speeds relative to the water as before. Their engines are switched off when they reach the buoy again If the maximum separation between the boats is 200 m after the buoy is dropped and water flow velocity is 1.5 m/s, find the distance between the two places where the boats meet the buoy is found to be 100 × n meters, the value of ‘n’ is .
If a particle is moving on a straight line, then its velocity time graph is sinusoidal as shown in the figure. The distance (in m) travelled by the particle in 2 s is .
If displacement of a particle is zero, the distance covered.
If the distance covered is zero, then the displacement
The numerical value of the ratio of displacement to distance is:
Which of the following velocity time graphs represent uniform motion.
Which of the following distance-time graph is not correct?
If the body moves with uniform velocity, then the acceleration of the body will be
If the body moves with uniform velocity, then the acceleration of the body will be
Fig shows the velocity time graph. This shows that the body is
Particle moving in a straight line is shown in fig. Corresponding acceleration versus velocity graph will be
The area under acceleration time graph gives
A body is projected vertically upwards and is reached to a vertical height of 20m and again reached the same point of projection. Then the distance travelled by the body is
A body goes 10 km north and then 10km east. What will be the distance covered from initial point?
A body travels along a semi-circles path of radius 10m. What is the distance covered by it
At the maximum height, of a body thrown vertically up……….
A car travels along a straight road 50m east then 20m west. Then the distance covered by the car
Car’s speedometer reads 9500km at the start of a trip and 10700km at the end.Find the distance covered by the car?
A body completes one round of a circular path of radius 5m. What will be its displacement
A body covered a distance of 10m along a semicircular path. The ratio of distance to displacement is:
A particle moves along x-axis in such a way that its coordinate (x) varies with time (t) according to the expression x = 6 t 2 + 5 t + 2 Its initial velocity is
A particle moves along a straight line such that the displacement at any time is given by S = 2 t 3 + 4 t 2 − 3 t + 5 m what is the velocity at t = 1 S
The position ‘ y ‘ of a particle varies with time (t) as y = a t 3 − b t 2 . The acceleration at time of the particle will be equal to zero, where ‘t’ is equal to
The Position of a particle as a function of time is described as y t = 3 t 2 + 2 t + 4 . What is the average velocity of the particle from t = 0 S t o t = 2 S
A car accelerates from rest to 30m/s in 5S . What is its acceleration
A car is decelerating from 20 m/s to rest in 10S. Determine its acceleration
The velocity time graph of the two particles A & B are shown in fig. The ratio of acceleration of the two particles at any instant is
The relation 3 x = 3 t − 6 describes the position of a particle in one direction where ‘x’ is in meters and t in sec . The displacement when velocity is zero, is……….
When the speed of a car is V, the minimum distance over which it can be stopped is x. If the speed becomes ‘nv’, what will be minimum distance over which it can be stopped during same time.
A person travels along a straight road for the first half time with a velocity 10m/s and the second half time with a velocity 20m/s . Then the mean velocity is given by
The displacement of a particle is proportional to the cube of the time. Then magnitude of its acceleration
A body moving with uniform acceleration of 5 m / s 2 changes its velocity from initial value of 10 m / s to final value of 30 m / s . Find the time taken by it
Moving with uniform acceleration, a body covers 150m during 10s so that it covers 24m during 10th sec. Find the initial velocity
A particle is moving with an initial velocity of 5m/s with uniform acceleration of 2m/s 2 . The distance covered by the particle in 3 rd second is….
A body released from certain height above the ground describes 7 16 of the total height in the last second of its fall. Then it is falling from a height equal to g = 9.8 m / s 2
In the last second of free fall, a body covered 3 4 t h of its total path. Then the height from which the body is released will be g = 10 m / s 2
The displacement ‘x’ of a particle at the instant when its velocity ‘v’ is given by v = 3 x + 16 m / s then its initial velocity in m/s
A food packet is dropped from a helicopter rising up with a velocity of 4m/s. The velocity of the packet after 3sec will be……..
A stone is projected vertically upwards with a speed of 29.4 m / s from the top of a tower of height 78.4 m . Then the time taken by it to reach the ground is……… g = 9.8 m / s 2
An object falls from a bridge that is 45m above the water. It falls directly into a small row-boat moving with constant velocity that was 12m from the point of impact when the object was released. What was the speed of the boat?
A ball is thrown upwards. It takes 6sec to reach back to the ground. Find its initial velocity. g = 10 m / s 2
If a ball is thrown vertically upwards with a speed ‘u’, the distance covered during the last ‘t’ seconds of its ascent is……..
A stone is allowed to fall from the top of a tower 300m height and at the same time another stone is projected vertically up from the ground with a velocity 30m/s .Find when the two stones meet?
A body is thrown vertically upward. At half of the maximum height, the velocity of the body is 10m/s. The maximum height reached by the body is
A body moves with initial velocity 10m/s. If it covers a distance of 20m in 2s, then the acceleration of the body is………..
A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in the displacement during the 4 th sec compared to that in the 3 rd sec is…
A body projected vertically up reaches a maximum height of 9.8 m. Its time of flight is g = 9.8 m / s 2
A person walks a distance of 40m towards west with a speed of 2m/s and 20m towards north with a speed of 4m/s. Then the average velocity for his journey.
A car moving on a straight road accelerates from a speed 5.1m/s to a speed of 7.9m/s in 3S. What is its average acceleration?
A proton in a cyclotron changes its velocity from 30km/sec north to 40km/sec east in 20sec. What is the magnitude of average acceleration during this time?
A body moving with uniform acceleration covers 100m in the first 10s and 150m in the next 10s. The acceleration of the body is
A body starts from rest and travels with a uniform acceleration of 5 m / s 2 and then decelerates at a uniform rate of 3 m / s 2 again to come to rest. Total time of travel is 10s . Then the maximum velocity attained by the body is
A person travels along a straight road for half of the distance with a velocity 30km/h and the remaining half distance with a velocity 50km/h. Then the average velocity is given by
If the distance travelled in nth sec is s n = 2 + 0.6 n . Find its initial velocity (in m/s)
A person travels along a straight road for the first half time with a velocity 45 m/s and the second half time with a velocity 10 m/s. Then the mean velocity is given by…….
A person travels along a straight road for half of the distance with a velocity 60km/h and the remaining half distance with a velocity 80km/h. Then the average velocity is given by………
Two balls are dropped from the same height at 1 second interval of time. The separation between the two balls after 3 seconds of the drop of the 1 st ball is……. g = 9.8 m / s 2
A body thrown upwards with some velocity reaches the maximum height of 50m. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of…………
A bullet emerges from a barrel of length 1.2m with a speed of 640 m/s. Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is……….ms
The distance travelled by a particle starting from rest and moving with a uniform acceleration of 4 3 m / s 2 in the 3 rd sec is…m
A helicopter is flying horizontally at 8 m/s at an altitude 180 m when a package of emergency medical supplies is ejected horizontally backward with a speed of 12 m/s relative to the helicopter. Ignoring air resistance, what is the horizontal distance between the package and the helicopter when the package hits the ground?
A very broad elevator plateform is going up vertically with a constant acceleration 1 ms -2 . At the instant when the velocity of the lift is 2 m/s, a stone is projected from the plateform with a speed of 20 m/s relative to the floor at an elevation 30 o . The time taken by the stone to return to the floor will be
The distance x covered by a body moving in a straight line in time t is given by the relation 2 x 2 + 3 x = t . If v is the velocity of the body at a certain instant of time, its acceleration will be
The variation in the speed of a car during its two hour journey is shown in the graph of Fig. The magnitude of the maximum acceleration of the car occurs during the interval
The displacement of a body from a reference point, is given by x = 2 t + 3 where x is in meter and t in seconds. This shows that the body is
A car is moving at a certain speed. The minimum distance over which it can be stopped is x. If the speed of the car is doubled, what will be the minimum distance over which the car can be stopped for the same retardation?
The distance x covered by a body moving in a straight line in time t is given by the relation 2 x 2 + 3 x = t . If v is the velocity of the body at a certain instant of time, its acceleration will be
A parachutist drops freely from an airplane for 10 s before the parachute opens. He then descends with a uniform retardation of 2.5 ms -2 . If he bails out of the plane at a height of 2495 m and g is 10 ms -2 , his velocity on reaching the ground will be
A ball is thrown upwards from the top of a tower of height 40 m with a velocity of 10 ms -1 . Find the time when it strikes the ground.
The displacement x of a particle varies with time according to the relation x = a b 1 − e − bt . Then take e − 1 ≃ 1 3
The maximum height attained by projectile is increased by 10% by changing the angle of projection, without changing the speed of projection. The percentage increase in the time of flight will be
A body is projected from the ground with a velocity u at an angle θ with the horizontal. The average velocity of the body between its point of projection and the highest point of its trajectory is
A particle travels first half of the total time with speed 20m/s and second half time with speed 30m/s. Find the average speed (in m/s) during complete journey.
A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speeds of 4.5 m/s and 7.5 m/s respectively. The average speed (in m/s) of the particle during this motion is
A body, moving in a straight line with an initial velocity of 5 ms -1 and a constant acceleration, covers a distance of 30 m in the 3 rd second. How much distance (in m) will it cover in the next 2 seconds?
Velocity of a particle moving in a straight line varies with its displacement as v = ( 4 + 4 s ) m / s . Displacement of a particle at time t = 0 i s s = 0 . Find displacement of particle at time t = 2 s .
From ground a balloon starts ascending at a constant speed of 25 m/s. After 5 sec a bullet is shot vertically upward from the ground. Find the minimum speed of bullet at which it is able to hit the balloon.
A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km h -1 . The jeep follows it at a speed of 90 km h -1 , crossing the turning 10 s later than the bike. The distance (in km) from turning point at which the police catch the culprit is .
A branch of physics dealing with motion without considering its causes is known as
A person walks up a stalled 15 m long escalator in 90 s . When standing on the same escalator now moving, the person is carried up in 60 s . How much time would it take that person to walk up the moving escalator? . Does the answer depend on the length of the escalator?
The variation in the speed of a car during its two hour journey is shown in the graph of Fig. The magnitude of the maximum acceleration of the car occurs during the interval
A bullet, incident normally on a wooden plank, loses one-tenth of its speed in passing through the plank. The least number of such planks required to stop the bullet is
The acceleration time graph of a particle moving in a straight line is as shown in figure. The velocity of the particle at time t = 0 is 2 m/s. The velocity after 2 s will be
A bullet when fired at a target with velocity of 100 ms -1 penetrates 1 m into it. If the bullet is fired at a similar target with a thickness 0.5 m, then it will emerge from it with a velocity of
For motion of an object along the x-axis, the velocity v depends on the displacement x as v = 3 x 2 − 2 x , then what is the acceleration at x = 2 m.
The velocity of a particle is v = v o + gt + ft 2 . If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is
A particle moving with a uniform acceleration along a straight line covers distance a and b in successive intervals of p and q second. The acceleration of the particle is
The retardation experienced by a moving motor boat, after its engine is cut-off, is given by dv dt = – kv 3 where k is a constant. If v 0 is the magnitude of the velocity at cut-off, the magnitude of the velocity at time t after the cut-off is
