Kinematics Questions and Answers

5 1 Two masses M and mare connected by a light string going over a pulley of radius r The pulley is free to rotate about its axis which is kept horizontal The moment of inertia of the pulley about the axis is I The system is released from rest Find the angular momentum of the system when the mass m has descended through a height h The string does not slip over the pulley

1 12 s 2 8 s 3 15 s 4 10 s 9 A particle moves along a straight line such that its displacement at any time t is given by s t 6t 3t 4 metres The velocity when the acceleration is zero is 1 3 m s 2 12 m s 3 42 m s 4 9 m s A point moves in a straight line so that its 20 19 442 dis 20 1 3 m s 3 42 m s 4

A pilot is supposed to fly east from A to B and back again A due west If the wind is blowing due south find time for the round trip if AB I The velocity of the plane in the air is v and the velocity of wind is u 1 21 2 u 3 1 v u 4 1 VP 1 1 v u

20 A point moves in a straight line so that its displacement x m at time t sec is given by x 1 t Its acceleration in m sec at a time t sec is 1 1 x 3 1 t X X 2 Ux 4 Both 1 and 3 20 as a re X X 1 1 x3 3 X X

10 A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with a speed of 15 ms The time taken by the stone to reach the ground is g 9 8 ms 1 10 s 2 5 s 3 12 s 4 15 s 10 Hell 490 15 ms l a 3241 2144 g 9 8 ms 1 10 s

An airplane moving horizontally with a speed 8 of 180 kmh drops a food packet while flying at a height of 490 m The horizontal range of the food packet is g 9 8 ms 1 180 m 2 980 m 3 500 m 4 670 m 180 kmh 243 414 4 9 di l g 9 8 ms 1 180 m

A body covers first one third of the distance with a velocity 10 ms in same direction the second one third with a velocity 20 ms 1 and last one third with a velocity of 30 ms 1 The average velocity of body is 1 17 8 ms 1 3 18 3 ms 1 2 16 4 ms 4 20 2 ms 1

Two balls are thrown vertically upwards simultaneously with different speeds The variation of their relative separation AY with time is best represented by Assume no rebouncing after hitting ground 1 3 MAY 2 MAY hh t MAY 4 MAY

A ball is thrown from a point with a speed vo at an angle of projection 0 From the same point and at the same instant a person starts running with a constant speed v 2 to catch the ball Will the person be able to catch the ball If yes what should be the angle of projection 1 Yes 60 2 Yes 30 4 Yes 45 3 No 7 1 0 ats Esit s Ag v 28241 el al E 1 l 60 3 LL

A cyclist starts from the centre O of circular path of radius 10 m covers the radius of circular path and reaches at point X on circumference then cycles along the semi circular path and reaches the point Y If he takes 10 minutes to go from O to Y via X then the net displacement and average speed of the cyclist would be 1 Zero 10 ms 3 10 m 7 ms 1 6 1 T 2 10 m 4 10 m 1 60 T 60 ms 1 ms 1

3 20 40 4 20 70 The maximum height reached by projectile is 4m The horizontal range is 12 m The velocity of projection in ms is g is acceleration due to gravity 1 5 g 2 3 g 2 2 3 g 2 4 g 2

1 4 ut t 3 u gt t 38 The displacement of a particle moving in a straight line depends on time t as x at Bt yt 8 The ratio of its initial acceleration to its initial velocity depends 1 only on a 2 only on a and B 3 only on and y 4 only on a and y

From the following velocity time graph body the distance travelled by the body a displacement during 5 seconds in metre be velocity m sec 40 30 20 10 10 20 30 40 1 75 75 3 110 110 15 t in sec 2 110 70 4 110 40

A bicycle rider Cyclist is traveling at a constant speed along a straight road and then gradually applie the brakes during a time interval 0 t t until the bicycle comes to a stop The combined mass the cyclist and bicycle is m Assume that the magnitude of the braking acceleration increases linearly i time according to a bt m bt m 0 t t where b 0 is a constant At the instant the cyclis applies the brakes at a particular horizontal distance from the him an iPod falls from the branch of th tree The Ipod was initially a height h above the ground The cyclist catches the iPod at the instant th cyclist has come to a stop You may assume that the cyclist catches it at a height s above the ground Lo h Which of the following statement s is are CORRECT A The time at which the cyclist catches the iPod is Ipod B The time at which the cyclist catches the iPod is C The initial speed of the cyclist is D The initial speed of the cyclist is b h s 2mg b h s 2 h s g h s g

3 2i j 4 5 i j 45 A person moving in straight line cover first half interval of time with speed x then in next half 45 interval he divide remaining distance in two equal parts and covers them with speed y and z respectively Average speed of total motion is 2x y z 2x y z 1 3 x y z 3 2 xy xz 2yz 2 y z 3xyz xy yz zx

0 the brakes during a time interval 0 t t until the bicycle comes to a stop The combined mass the cyclist and bicycle is m Assume that the magnitude of the braking acceleration increases linearly i time according to a bt m 0 t t where b 0 is a constant At the instant the cyclis applies the brakes at a particular horizontal distance from the him an iPod falls from the branch of th tree The Ipod was initially a height h above the ground The cyclist catches the iPod at the instant th cyclist has come to a stop You may assume that the cyclist catches it at a height s above the ground h ent s is are COR Ipod Which of the following statement s is are CORRECT A The velocity of iPod at the instant cyclist catches it is 2 h s g b B The distance travelled by the cyclist till the instant he catches iPod is 3m C The velocity of iPod at the instant cyclist catches it is h s g h s g Taa 13 2 73 2

A river is flowing at 3m s A boat can move at 5 m s in still water Boat starts from point A Select the correct statement s given width of river 120m V 3 m s A A Boat can cross the river in minimum time 24 sec B Drift of the boat is zero if it starts at 127 from the direction of flow C If boat is started perpendicular to the flow w r t river then it will appear to move at 37 from direction of river flow for the ground observer D If boat crosses the river in minimum time drift of boat will be 72 m

A spherical object is of diameter d and density p The diameter is such that it equals De Broglie wavelengths of the object when the object falls through vacuum in the gravitational field of the earth through a distance d Then d is equal to Question Type Single Correct Type 1 2 3 d d d 9h p g 18h g 1 9 1 6 1 9 6h 515 3

A man crosses a river of width d Current flow speed is v Speed of swimmer relative to water is v Man always head towards the point exactly opposite to the starting point at the another bank relative to water If radius of curvature of the path followed by the swimmer just after he start yimming is

9 What is are the possible velocity time graph graphs if particle moves in a straight line path according to the distance time graph A C a distance F B straight line D parabolic parabolic time V a

25 Velocity of a particle is v 2x m s where x is position in metre then find acceleration of this particle at x 1m 1 2 m s 2 3 m s 4 4 m s 3 6 m s 26 A particle moves along the x axis such that

The velocity of a body changes from 4 m s to 10 m s in 3 s It covers a distance of x m in 3rd second its motion The distance covered in the 5th second of its motion is 1 xm 2 x 2 m 3 x 4 m 4 x 6 m

1 2 3 3 6 A body starts from the origin and moves al the x axis that the velocity at any instant is gi by v 41 2t v is in m s What is acceleration of the particle when it is t 1 sec 1 28 m s 2 10 m s 3 12 m s 4 20 m s car moving on a straight road covers hal

C Lies between 60 and 120 D Depends on x A particle moves in space such that x 2t 3t 4 y 4t 1 z 2 sin at where x y z a measured in meter and t in second The acceleration of the particle at t 3s is A 361 2j k B 361 21 rk ms C 361 2 ms D 121 2 ms 2 ms

A man can swim at 2 m s in a swimming pool He enters a 100 m wide river at one bank and swims at right angles to the river flow velocity w r t water If his drift on reaching the other bank is 40 m calculate the river flow velocity A 0 4 m s B 0 8 m s C 0 6 m s D 2 m s

3 12 m s 4 20 m s 37 A car moving on a straight road covers half a certain distance with a speed of 40 km h a the other half with 60 km h Then its avera speed is 1 40 km hr 3 46 km hr 2 80 km hr 4 48 km hr

CAREER INSTITUTE AKINETRARE 33 In 2 0 second a particle goes from A to point B moving on a semi circle of radius 4m the magnitude of average velocity is A 34 4m BL 1 4 m s 2 2 m s 3 2 m s 4 zero A particle is moving on x axis of a reference

4 depends upon the particle 31 A body moves 4m towards east and then 3 m north The displacement and distance covered by the body are 1 7m 6m 3 5 m 7m 2 6m 5m 4 4m 3m

A particle is moving at a constant velocity v A constant force F is then applied to the particle After t seconds elapse the speed of the particle is halved After another t seconds elapse the speed of the particle is halved again What is the speed of the particle v after t more seconds elapse A 8 B 7 4 V C 2 D such a situation is not possible

23 Ball A is projected from tower of height 30 m and B is projected horizontally at 6 m s from tower of height 60 m If A and B collide in air then find the separation d between the towers in meters CENTERS MUMBAI DELHI AKOLA LUCKNOW NASHIK PUNE NAGPUR BOKARO DUBAI 4 A 30 m s 53 6 m s B 60 m

A particle is contrained to move on a straight 32 line path It returns to the starting point after 10 sec The total distance covered by the particle during this time is 30 m Which of the following statements about the motion of the particle is false 1 Displacement of the particle is zero 2 Average speed of the particle is 3 m s 3 Displacement of the particle is 30 m 4 Average velocity is zero

Four particles A B C and D are moving with constant speed v each At the instant shown relative velocity of A with respect to B C and D are in directions C 1 2 3 B Question Type Single Correct Type

8 The position of x of a particle varies with tim t as x at bt Find velocity of the particle when acceleration of the particle is zero 1 2a 3b 2 a 3b 3 3b 4 3b

fun drive in an amusement park runs between two spots that are 2 0 m apart For safety reasons acceleration of the drive is limited to 14 C n s2 and the jerk i e rate of change in acceleration is limited to 1 0 n s If the drive can achieve a maximum speed of 144 km h find the hortest transit time of the drive between the spots

A river is flowing at 3 m s towards East a boat is steered toward North at 4 m s and wind is blowing at 5 m s 53 North of East Flag mounted on boat will flutter along B D North East South West West Stand still

Solvelancer Test Consider a particle of mass 2 kg In first reference frame the velocity of the particle is 4 m s The second reference frame is moving with velocity 3 m s Find the kinetic energy of the particle as seen from second reference frame SolveLancer Test a 50 J b 9 c 25 J d 1 I

A 10 km long straight road connects two towns A and B Two cyclists start simultaneously one from town A and the other from town B On reaching the opposite town a cyclist immediately returns to his starting town whereas the other cyclist takes some rest and then returns to his starting town Both of them can ride at a speed 20 km h in absence of wind but during their whole journey uniform wind from town A to B increases speed of a cyclist going with the wind by the same amount as it decreases the speed of the cyclist going against the wind Both the cyclists meet twice first 2 km and then 6 km away from one of the towns In which town and for what period a cyclist rests

A block is placed on top of a fixed smooth inclined plane inclined at 30 to horizontal The length of plane is 5 m The block slides down the plane and reaches at bottom The speed of the block at bottom will be nearly 1 6 m s 3 3 5 m s 5 m 30 m 2 7 0 m s 4 9 2 m s

Kelative Motion and Changing FOR Problems A 600 m wide river flows at 6 50 m s W wrt the ground A boat on the river moves at 15 0 m s wrt to the wate The boat leaves the south shore and lands on the north shore For each landing position relative to the start position calculate the required velocity of the boat wrt the water and the time interval required to cross the river a Ad 0 m b Ad 100 m W c Ad 500 m W

O O O will always observe colour shift for a o motion may observe no variation in velocities fo same object in motion may observe variation in velocities for a object in motion

Two trains one travelling at 15 m s and the other at 20 m s are headed towards each other on a level track When they are 2 km apart both drivers apply simultaneously brakes If their brakes produces retardation of 0 20 m s for each The final separation between trains is 1 468 8 m 2 203 3 m 3 605 5 m 4 Zero 4

A ball is thrown in the air and returns to the same level ground following a parabolic path Which one of the following does not have the same value at the time of throw and at the time of return to ground 1 Kinetic energy of the ball 2 Speed of the ball 3 Vertical component of velocity 4 Horizontal component of velocity A sphere is attached to an input

An object thrown vertically upward reaches to a maximum height of 125 m Choose the incorrect option a initial speed of object is 50 m s B total time for which object remains in air i s 10 sec C distance travelled by object in the last se cond of it s upward journey is 0 5 m D time of ascent of object is 5s

A 150 m long train moves towards south at a speed of 10 m s A sparrow flying at a speed of 5 m s towards north crosses the train What is the time taken by the sparrow to cross the train O 30 s O 15s O 00 02 8s

Four position time graphs are shown below Which of them has positive non zero average velocity i x m Z t s iii x m A i and ii t s B ii and iv ii x m iv x m S t s t s 1 C i ii and iv D All of them

B On the same vertical line two points P and Q P above Q are present An object is thrown vertically upwards in such a way from Q that it can only rise up to P At the same moment another object is dropped from P Show that when the two objects meet i they have equal and opposite velocities and ii ratio of the dis tances traveled by them is 3 1

Mayank give a situation to his student that there are four particles A B C and D and their relative velocities are given as Vpc 20 m s toward the north VBC 20 m s towards the east and VBA 20 m s towards the south Then VDA is O O O 20 m s north 20 m s south 20 m s east 20 m s west

Two bikes travelling in the same direction move at a speed of 30 km hr The bikes are separated by a distance of 5 km What would the speed of the car travelling in the opposite direction be if it meets these bikes at an interval of 4 minutes O O 40 km hr a 45 km hr O 30 km hr 15 km hr

A man on moving plank A throws a bal l of mass m with horizontal compone nt of velocity u 3 34 m s with respect to ground towards the stationary plank B as shown in the figure While the ma n on plank B catches the ball The com bined mass of plank A with man is 2 m and combined mass of plank B an d man is also 2m Initially plank A is moving with speed u with respect to gr ound along positive x axis in direction and there is no friction between plank a nd ground Assume xy plane to be verti cal The relative velocity of B with respe ct to A after man on B catches the ball

arrow is shot from a height of 1 6 m toward a cliff of height H It is shot with a velocity of 35 m s at an angle of move the horizontal It lands on the top edge of the cliff 3 91 s later