Kinematics Questions and Answers

8 A body initially at rest is moving with uniform acceleration a Its velocity after n seconds is v The displacement of the body in last 2 s is 2v n 1 v n 1 b a 1 v n 1 FI 2v n 1 c d 11 11 A body A starts from rest with an acceleration du 84 A ball Ai At the san rest at hei Bis a u c 85 Two cars km h am 1 of car A

67 A ball is thrown vertically upwards with a velocity of 20 m s from the top of a multistorey building of 25 m high How high will the ball rise Take g 10 ms a 10 m c 20 m b 15 m d 25 m 68 In the question number 67 the time taken by the

A police jeep is chasing culprit going on motorcycle The motorcycle crosses a turning at 20 m s The jeep follows at speed of 30 m s crossing the turning 6 second later than motor cycle If they travel at constant speeds how far from turning point jeep catches up the motorcycle 40 m 50 m 360 m 120 m

69 Two trains A and B each of length 400 m are moving on two parallel tracks with a uniform speec 72 km h in the same direction with A ahead of B The driver of B decides to overtake A and accelerates by 1 ms If after 50 s the guard of B just brushes past A what was the original distance between them a 750 m c 1250 m b 1000 m d 2250 m

71 A body covers a distance of 4 m in 3rd second and 12 m in 5th second If the motion is uniformly accelerated how far will it travel in the next 3 seconds a 10 m c 40 m b 30 m d 60 m

37 61 A player throws a ball upwards with an initial speed of 30 m s How long does the ball take to return to the player s hands Take g 10 ms a 3s c 9s b 6 d 12 s g same for both I

numbers S A body covers 20 m 22 m 24 m in 8th 9th and 10th 64 It is a seconds respectively The body starts at abe a from rest and moves with uniform velocity b from rest and moves with uniform acceleration c with an initial velocity and moves with uniform acceleration d with an initial velocity and moves with uniform velocity 57 drop then Take a 5 c 7 65 A ma

54 Which of the following statements is not correct a The zero velocity of a body at any instant does not necessarily imply zero acceleration at that instant b The kinematic equation of motions are true only for motion in which the magnitude and the direction of acceleration are constants during the course of motion c The sign of acceleration tells us whether the particle s speed is increasing or decreasing d All of th 61 62

8 The speed time graph Speed ms ofa particle moving along a fixed direction is shown in the figure The distance traversed by the particle between t 2s to t 6s is a 26 m b 36 m c 46 m ysics Tume s d 56 m Motion in a Straigh 54 Which of th a The zer not nec instant b The kir only for directio

d the velocity of the ball is u but its acceleration is g 58 A car moving along a straight road with speed of 144 km his brought to a stop within a distance of 200 m How long does it take for the car to stop a 5 s b 10 s c 15 s d 20 s

b 4 5 s c 3 6 s d 7 0 s 60 A body falling freely under gravity passes two points 30 m apart in 1 s From what point above the upper point it began to fall Take g 9 8 m s2 a 32 1 m b 16 0 m c 8 6 m d 4 0 m a c 68 In S bal a c

celeration for t s It travels a distance x im If of time and x in next half of time then x 3x b x x

A force of 1 N acts on a 1 kg mass for 1 second which is initially at rest In another case 1 N force acts on 1 kg mass which is initially at rest and moves it through 1 m The ratio of kinetic energy in the two cases is O 1 1 O 1 2 1 4 O 1 2

36 The graph of velocity displacement a particle is as shown in the figure Which of the following graphs correctly represents the variation of acceleration with displacement a c b d 46 The velocity time graph of a 1 49

27 The position time x t graphs for two children A and B returning from their school O to their homes P and Q respectively are as shown in the figure Choose the incorrect statement regarding these graphs a A lives closer to the school than B b A starts from the school earlier than B c A walks faster than B d A and B reach home at the same time 71 b

A car starts from rest and reaches a speed of 50 m s in 6 seconds It continues at this speed for a further 5 seconds before coming to a halt 7 seconds later a Draw a speed time graph for the car b What was the car s initial acceleration c What was the car s final deceleration

fall vertically downwards When he increases his speed to 6 km h it appears to meet him at an angle of 45 with vertical Find the speed of rain Solution Let i and j be the unit vectors in horizontal and vertical directions respectively Vertical 1 A Is it clockwise or anticlockwise from the vertical Let velocity of rain Then speed of rain will be In the first case Hence In the second case It seems to be in vertical direction Mechanics I 150 il rm Horizontal m velocity of man 31 V Vm a 3 i bj Fig 6 60 v ai bi v a b a 3 0 or a 3 Vrm a 6 i b 3 b

Motion in a Straight Line 34 The slope of the tangent drawn on velocity time graph at any instant of time is equal to the instantaneous a acceleration c impulse 35 The area under acceleration time graph represents the a initial velocity c change in velocity b velocity d momentum 36 Which of the following statements is not correct regarding the motion of a particle in a straight line a x t graph is a parabola if motion is uniformly 40 accelerated b v t is a straight line inclined to the time axis if motion is uniformly accelerated A b final velocity d distance travelled c x t graph is a straight line inclined to the time axis if motion is uniform and acceleration is B C D d A car starts from rest attains a velocity of 36 km h with an acceleration of 0 2 m s2 travels 9 km with this uniform velocity and then comes to halt with a uniform deceleration of 0 1 m s2 The total time of travel of the car is a 1050 s zero c 950 s d v t graph is a parabola if motion is uniform and 41 A particle moving with uniform acceleration has acceleration is zero average velocities v V and v over the successive intervals of time t f and t respectively The value 37 Match the Column I with Column II Column I of will be Graph Column II Characteristic p Has v 0 and a 0 throughout q Has x 0 throughout and has a point with v 0 and a point with a 0 r Has a point with zero displacement for t 0 s Has v 0 and a 0 How a 2 ms c 1 ms a A p B q C s D r b A q B p C r D s c A s B r C q D p d A r B q C s D p 38 A particle moving along a straight line has a velocity vms when it cleared a distance of x m These two are connected by the relation v 49 x When its velocity is 1 m s its acceleration is 7 A particle moves rectilinearly Its displacement x at time t is given by xat b where a and b are constants Its acceleration at time t is proportional to a v 2 V V a 5 1 1 13 c 5 1 1 13 b 7 ms 2 d 0 5 ms a P 9 b c 1 b 1000 s d 900 s b A particle starts from point A moves along a straight line path with an acceleration 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 particle is b L 44 Position time graph acceleration is l 1 d 1 1 1 35 c 9 P P For the one dimensional motion described by x t sint a x t 0 for all t 0 c a t 0 for all t 0 b d b v t 0 for all 1 0 d all of these for motion with zero d L X

59A particle moves rectilinearly Its displacement x at time t is given by x at b where a and bare constants Its acceleration at time t is proportional to a 1 1 c b d 1 1 40 A car starts from rest attains a velocity of 36 km h

36 Which of the following statements is not correct regarding the motion of a particle in a straight line a x t graph is a parabola if motion is uniformly accelerated b v t is a straight line inclined to the time axis if motion is uniformly accelerated c x t graph is a straight line inclined to the time axis if motion is uniform and acceleration is zero d v t graph is a parabola if motion is uniform and acceleration is zero 37 Match the Column I with Column II

28 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 Displacement t Time a C c E 29 In the given v t graph the distance travelled by the b D d F

c 60 m d 80 m D 31 Which of the following graphs cannot possibly represent one dimensional motion of a particle 0 Speed iii a i and ii c i ii and iii ii Total path length W iv b ii and iii d All four ACCELERATION S the a i c c 36 Whis regar a x b c d 37 Mate A

A 10 metric ton truck drives up a hilly road of inclination 45 at a speed of 36 km h If the coefficient of kinetic friction between the road and tyres is 0 2 calculate how fast will the same truck move down the hill with same power 48 km h 72 km h 54 km h 36 km h

with same speed of 20 m s at time t 0 Ball A has an initial horizontal velocity and ball B has initial velocity at an angle e above the line joining A and B as shown in the fig If the projectiles collide in mid air at time t then c Sr Super60 All Chaitanya IIT Academy Space for rough work A Page 4 06 06 2021 Sr Super60 All Jee Adv 2018 P1 GTA 08 Q P 20 m s

c i iii and iv d All four 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 Qin 6s Which of the following statements is not correct regarding the motion of the car 0 P Om 240 m 360 m a The average speed of the car in going from 0 to P and come back to Q is 20 m s b The average velocity of the car in going from O to P and come back to Q is 10 m s

ACCELERATION Mak 2 The displacement of a body is given to be proportional to the cube of time elapsed The magnitude of the acceleration of the body is a increasing with time b decreasing with time c constant but not zero d zero E

time to and then stops 26 Figure shows the x t plot of a particle in one dimensional motion Two different equal intervals of time are shown Let v and v be average speed in time intervals 1 and 2 respectively Then a v V c V V 7 The position time x t graphs Z b v V d data is insufficient rep

speed may be variable The position of an object moving along x axis is given by x a be where a 8 5 m and b 2 5 ms2 and t is measured in seconds The instantaneous velocity of the object at t 2 sis a 5 ms 1 b 10 m s c 15 m s d 20 m s 1x1 0 The motion of a particle is described by the equation

c 4 4 d 1 13 A particle starts from point A moves along a straight line path with an acceleration 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 particle is a P 9 c 9 P d 9 P

A particle moving with uniform acceleration has average velocities V V and v over the successive intervals of time t t and t respectively The value of will be V V a 4 4 1 13 c 4 4 b 4 h t 1 d 1 t ty A particle starts from point A moves along a straight line path with an acceleration given by a p qx

varies with time as a v 1 c v 1 b v 2 1 e d v 2 1 4 The position x of a particle with respect to time t along x axis is given by x 9t Pwhere x is in metres and t is in seconds What will be the position of this particle when it achieves maximum speed along the x direction a 54 m c 24 m b 81 m d 32 m

34 25 Figure shows the displacement x time 1 graph of the particle moving on the x axis a The particle is at rest b The particle is continuously going along x direction c The velocity of the particle increases upto time to and then becomes constant d The particle moves at a constant velocity up to a time fo and then stops 3 3

c 15 m s d 20 m s x 0 The motion of a particle is described by the equation xat bt where a 15 cm s and b 3 cm s Its instantaneous velocity at t 3s will be a 33 cm s 1 c 16 cm s b 18 cm s 1 d 32 cms t

to a ding valks erage 0 23 The motion of a body is given by the equation dv 2 6 3v where v is the speed in m s and t is dt time in s The body is at rest at t 0 The speed varies with time as a v 1 b v 2 1 c v 1 2 d v 2 1 24 The position x of a particle with respect to time t

a zero b 4 ms c 2 ms d 8xms 2 The position of an object moving along x axis is given by x a br where a 8 5 m and b 2 5 m s2 and t is measured in seconds The average velocity of the object between t 2 s and t 4 sis a 5 ms c 15 m s b 10 m st d 20 m s

4 A body moving along a straight line travels one third of the total distance with a speed of 3 0 m s The remaining distance is covered with a speed of 4 0 m s for half the time and 5 0 ms for the other half of the time The average speed during the motion is a 4 0 ms c 3 8 m s b 6 0 m s d 2 4 m s

14 f A B C 0 then AxB iste 1 CXB South CD cos 0 2 BxC 4 Zero BAXC C DX 15 If the angle between the vectors C and D is 0 then the value of the product x is equal 1 Zero 2 CD2 sin 8 CD2 sin 8 cos e 4

Figure shows a quarter circle A particle move from B to O with 5 m s from O to A with 7 m s With what speed the particle should move from A to B so that average speed for total journey is 6 m s 1 3 210 4 35 38 T 210 TU 4 B m s m s 2 4 A 210 4 31 T 205 35 TU 4 m s m s

An object of mass m initially at rest under the action of a constant force F attains a velocity v in time t and covers a distance L Then the average power supplied to mass is mvL Fv 2 Both 1 2 Neither 1 por 2

D 7 In the figure shown the velocity of lift is 2 m s while string is winding on the motor shaft with velocity 2 m s and block A is moving downwards with a velocity of 2 m s then find out the velocity of block B 12m s A 2 m s B 2 m s 2 m s BCA 2m s C 4 m s D 0 m s D 8 m s

A boy is standing on a flatcar that is moving with uniform acceleration on a level track At the instant when flatcar is moving with velocity 10 m s due east the boy throws a ball with velocity 20 m s in direction 15 above the east with respect to the flatcar in plane of motion of flatcar What should be the acceleration of the flatear so that the boy can catch the ball without moving anywhere on the flatcar Assume acceleration due to gravity 10 m s A 10 m s eastwards B 10 m s westwards C 20 m s castwards D 20 m s westwards

t 3 If two persons P and Q start at the same time in opposite directions from two points and after passing each they complete their journeys in a and b hrs respectively then P s speed Q s speed a

A drunkard walking in a narrow lane takes 5 steps forward 3 steps backward and then stay for 1 s and repeat the same process again and again Each step is 1 m long and takes 1 s The time taken by drunkard to fall in a pit 10 m away from start is 1 45 s NCERT Pg 56 2 27 s

4 During the Egg Throwing Demonstration a Which egg experienced the greater impulse the egg that hit the wall or the bed sheet Be careful here Explain how you know b Which egg experienced the greater force of impact Why c Which egg experienced the greater time of impact Why

a bullet that leaves the muzzle of a gun at 250m s is to hit a target 100m away at the level of the run must be aimed at a point above the target How far above the target is that point

A and B starts from rest and moves with acceleration ratio 4 9 If distance covered by A is 25 of distance covered by B then find the ratio of time required by B and A SolveLancer Test a 3 4 b 4 3 c 2 3 d 3 2

Question No 16 A free falling body takes 6 s to reach the ground Three second after release the percentage of retained potential energy to its initial potential energy is O 60 75 40 80

8 When a body is projected vertically upwards from the of a tower it reaches the ground in seconds However when it is projected straight downward with the same speed it reaches the ground in 2 seconds How much time the body would take if it is simply dropped from the top of the same tower

6 A projectile is thrown with speed 60 m s at 60 from the horizontal It will be at same heights a instants g 10 m s 3 1 7 1 t 4 5 s t 6 5 s 2 t 3 2 s t 6 8 s 3 t 3 1 s t 7 1 s 4 t 2 s t 6 s

A particle is moving with uniform acceleration along x axis with initial velocity along positive x A 3 2 s the magnitude of displacement becomes 2 1 coordinate of particle is still positive The instant in sec at which displacement becomes zero is t T 1 the total distance travelled By this time the 3