Kinematics Questions and Answers

The velocity v time t graph for a particle moving along x axis is shown in the figure The average velocity in the time interval t 0 to t 8 s is v m s 10 0 10 4 5 m s 2 5 m s 5 m s O 2 m s 6 8 t s

3 2mv 4 2mv A body of mass mis projected with initial speed u at an angle with the horizontal The change in mome body after time tis 1 musino 3 mat 2 4 2musing 7m

3 30 kgm s 4 50 30 kg m s A cart loaded with sand moving with velocity v Sand is falling through the hole as shown in diagram then after falling on the ground sand is 1 Moving with cart 3 Stationary on the ground Smooth surface 2 Moving in opposite direction with speed v 4 Moving with speed Y

60 s making an angle of 30 with vertical towards south alling with a speed of 4m s is a direction What should be the magnitude and direction of velocity of cyclist to hold his umbrella exactly vertical so that rain does not wet him 1 2m s towards north 2 4m s towards south 3 2m s towards south 4m s towards north

A man can swim at a speed of 5 km h w r t wate He wants to cross a 1 5 km wide river flowing at km h He always keeps himself at an angle of 60 with the flow direction while swimming The time taken by him to cross the river will be 1 0 25 h 2 0 35 h 3 0 45 h 4 0 55 h Two particles 1 and 1 the

A solid sphere is thrown up a rough incline The sphere rolls up without slipping and eventually comes down rolling without slipping The direction of rolling friction in upward and downward motion respectively is

velocity of particle chan projected from ground till it lands on ground as shown in figure is 2m s find maximum height of the projectile g acceleration due to gravity If magnitude 1 611 E 2 2 1 4g m

ms 1 4 5 4 ms 1 a man walking due west with a speed of 4m s wind appears to blow from the north east when he increases his speed to 7m s the wind appears to blow from the north Find velocity of wind with respect to ground 1 50 3 58 swimmer heads directly 1 6 m s relative downstr 2 40 4 42

35 A train moves at 15 0 m s in the x direction A child on the train drops a ball out the window with zero initial y component of velocity From the child s point of view the ball falls straight down to the ground An observer standing on the ground also watches the ball drop She observes that the ball hits the ground 12 0 m along the x axis ahead of the drop point Neglect friction 15 m s 12 m a From what height above the ground was the ball dropped b According to the ground observer what is the instantaneous velocity vector v of the ball just before it hits the ground Express v in terms of unit vectors i and j c According to the ground observer what is the average velocity vector Vay of the ball over the time of its fall Express Vav in terms of unit vectors i and j d According to the ground observer what is the average acceleration vector aav over the time of its fall Express aay in terms of unit vectors

Negative Marks 1 If wrong option is selected A small particle of mass m attached with a light inextensible thread of length L is moving in a vertical circle In the given case particle is moving in complete vertical circle and ratio of its maximum to minimum velocity is 2 1 Minimum velocity of the particle is 4 2 gL gL 3 gL V 3

A motorboat is racing towards North at 25km h and the water current in that region is 10km h in the direction of 600 east of south The magnitude of resultant velocity of the boat is B C D 11 km h 32km h 11 km h 22 Km h

A particle of mass 1 kg is given a horizontal velocity of 4 m s along a horizontal surface with which it has a coefficient of friction both static and kinetic of 0 4 The particle strikes a fixed ideal spring of force constant 6 N m after traveling a distance of 0 25 m Assume acceleration due to gravity is 10 m s Find the maximum displacement of the particle from its starting point g 10m s O O 9 8 V 3m 8 83 7 73 V3 0 25m 0 25m 4 m s 1 kg u 0 4 0 25m lllllllll

The acceleration a time t graph of a particle moving in a straight line is as shown in figure At time t 0 the velocity of particle is 10 m s What is the velocity at t 8 s NCERT Pg 45 a m s 4 2 O 2 4 6 2 4 6 8 t s

Pls explain why we need to substract 280 60 kg as give n in ncert od 1 8 x 10 N Example 9 3 In a human pyramid in a circus the entire weight of the balanced group is supported by the legs of a performer who is lying on his back as shown in Fig 9 5 The combined mass of all the persons performing the act and the tables plaques etc involved is 280 kg The mass of the performer lying on his back at the bottom of the pyramid is 60 kg Each thighbone femur of this performer has a length of 50 cm and an effective radius of 2 0 cm Determine the amount by which each thighbone gets compressed under the extra load A Us thi d O

A vehicle was moving at 32 km h 1 towards north A passenger noticed that rain was striking his body from the east When the velocity of the vehicle was increased to 64 km h rain appeared to come from the north east direction Find the actual velocity and direction of rain 32 2 km h 1 from south east

8 Rain is falling vertically with a speed of 43 m s A woman rides a bicycle with a speed of 14 m s in west to east direction Find the direction in whic she should hold her umbrella

The friction coefficient between the surface and the blocks is 0 2 At initial moment blocks are separated by 16cm and 2kg block is moving with a speed of 1m s towards 4kg block which is at rest as shown Collision between the blocks is perfectly elastic Find separation in cm between them when they come to rest after collision g 10m s 2kg 1 m s 16 cm At rest 4kg

Two particles start moving along the same straight line starting at the same moment from the same point in the same direction The first moves with constant velocity u and the second with constant acceleration f During the time that elapses before second catches the first the greatest distance between the particles is A f 24 C B D 2f f

13 If initial velocity of particle is 2 m s the maximum velocity of particle from t 0 tot 20 sec is 1x2x2m 2m tam zd xxx 4 2x22 16 20 4n 897 8 2 1 20 m s 3 22 m s 31 8 10 12 4x 42 16m x 4 7 8mls 2 18 m s girls 4 24 m s 1x2x4

At t 0 a block of mass m is projected with speed v on a rough long plank of mass 3m placed on smooth ground as shown Work done by friction on the block between t 0 until slipping ceases equals Rough A B C D 15 32 mv 15 32 my mv 16 my O m 3m Smooth

block is thrown on a fixed inclined as shown with initial velocity v 20 m s What will be the acceleration in m s of block 2 sec after it leaves the contact from incline g 9 8 m s 2 smooth 0 45 fixed 10m

A particle is moving in xy plane crosses the origin at time t 0 The equation motion of the particle is y 4 x If the velocity of the particle is v 274 27 m s a m s then the magnitude of a is and acceleration is a

A block is thrown on a fixed inclined as shown with initial velocity Vo 20 m s What will be the acceleration in m s of block 2 sec after it leaves the contact from incline g 9 8 m s smoot Vo 45 V fixed 10m A

system you chose b Consider two scenarios A ball of weight 10 N rolls on the floor and a block of weight 10 N slides on a table In which case will the applied force required to just set the body im motion greater Why

A par mass 3 kg is moving plane such that x t 2 sin 2t y t t 4t and z t 5 If all measurements are in Sl units then Total acceleration of particle at t sec is along y axis Velocity of particle at t 0 is v 41 4 Acceleration of particle at t 0 is 81 61 Particle is under constant acceleration A

Two trains 100 m and 80 m long respectively are running in opposite directions Trains A running with constant velocity 10 m s and train B start from rest and running with uniform acceleration 5 m s2 If the initial separation between two trains is 80 m Then after what time they meet each other In second

The diagram below shows a block on a horizontal frictionless ground Other than its weight W normal reaction N from ground and the 100 N force at angle of 30 above the horizontal additional force F also acts on the block If the block remains in equilibrium which of the following statements should be correct 30

left n e 0 is iii An aircraft is descending to land at an airport in the morning The aircraft is landing to the east so that pilot has the sun in his eyes The aircraft has a speed v and is descending at an angle a and the sun is at an angle above the horizon Find the speed with which the aircraft s shadow moves over the ground v cosa sina cot

A body of mass 2kg has an initial velocity of 3 m s along OE and it is subjected to a foce of 4 newtons in a direction perpendicular to OE The distance of body from O after 4 seconds will be 1 12 metres 3 8 metres When 2 20 metres 4 48 metres

result in 2 marks A particle of mass 5 kg is moving in x y plane such that x t 2 sin 2t y t t3 4t and z t 5 If all measurements are in SI unit then Total acceleration of particle at t sec is along y axis Velocity of particle at t 0 is v 41 4 DAcceleration of particle at t 0 is 81 6 O Particle is under constant acceleration motion

4 a body moving with a variable speed has zero acceleration What will be the angle between two forces of equal magnitude if the magnitude of resultant for s equal to any one of the two 1 0 3 90 2 60 4 120

A passenger in a uniformly moving train throws a ball upwards The ball will return 1 in the passenger s hand 2 by the side of the passenger 3 in front of the passenger in direction of motion 4 Behind the passenger in the direction opposite to the motion of train

bod The correct statement in the following is 1 a body can have acceleration even if its velocity is zero 2 if the velocity of the body be zero it will necessarily have acceleration 3 if the speed of a body is constant its acceleration also will be constant 4 a body moving with a variable speed has zero acceleration places

A car is moving on a straight road at a speed of 50 km h and a truck is ahead of the car and having a large plane mirror fixed vertically on the back of the truck Truck is running at a speed of 70 km h For a stationary observer standing between car and truck What is the speed of the image of the car in the mirror 1 40 km h 2 70 km h 3 20 km h 4 90 km h 1 2 We see that your answer is incorrect Please mention reason from below 3 4

A plane flying horizontally at a height of 320m at a speed of 120m s wishes to hit a tank that is moving away from it in the same direction on the ground with a speed of 5m s At what horizontal distance from the tank should the plane release its bomb

ILLUSTRATION 1 A rod of mass M m and length carries an insect of mass m at its bottom end and top end is connected with a string which passes over a smooth pulley and other end of the string is connected to a counter weight of mass M Initially the insect is at rest Rod M m Insect Counterweight M If we consider insect rod counter weight as system a Is there any net external force acting on the system initially b If the insect starts crawling up on the rod with constant velocity whether the centre of mass of the system accelerates or not c If the insect moves up with acceleration does the centre of mass of the system accelerate d Find the displacement of centre of mass of the system when the insect reaches to the other end of the rod e Find the displacement of the rod when the insect reaches

Two masses M to M connected by means of a string which is made to pass over light smooth pulley are in equilibrium on a fixed smooth wedge as shown in figure If 0 60 and a 30 then the ratio of M to M is A 1 2 B 2 3 C 1 3 D 3 1

Two particles A and B situated at 0 4 m and 3 m 0 start moving with constant speed 10 m s and 5 m s respectively Direction of velocity of B is always along the vector while direction of velocity of particia A is always towards the particle B If after time to both the particles meet with each other then average velocity of A in the time interval to is 1 171 31 m s a 31 7 m s 2 17 1 3 m s 4 3i 171 m s

34 A simple pendulum suspended from the ceiling of a stationary lift has period To When the lift descends at steady speed the period is T and when it descends with constant downward acceleration the period is T Which one of the following is true 1 To T T 3 T T T 2 T T T 4 To T T

Two small bodies of masses m and 2m are placed in a fixed smooth horizontal circular hollow tube of mean radius r as shown The mass m is moving with speed u and the mass 2m is stationary After their first collision the time elapsed before next collision is coefficient of restitution e 1 2

Two projectile X and Y thrown with speeds u and U 2 is acquired the same maximum heights If X throw an angle 60 with the horizontal the angle of projection of Y with the horizontal was 1 60 2 45 3 37 4 30

A boat takes 2 hours to go 10 km and come back in still water lake The time taken for going 10 km upstream and coming back with water velocity of 5 km h is 1 140 min 2 150 min 3 160 min 4 170 min

34 A small stone is dropped from the top of a ladder falls and hits the ground It does not rebound Which speed time graph is correct A speed of stone speed of stone C time time speed of stone speed of stone B D time time

2 When a body is projected vertically up from the ground its velocity is reduced to rd of its initial velocity at height habove the ground Then maximum height reached by the body is 1 3h 2 4h 3 9h 9h

A projectile is fired at an angle of 0 45 above the horizontal with a speed of v 9 9 m s At the highest point of its trajectory the projectile explodes into three fragments with equal mass two of which fall vertically with zero initial speed You can ignore air resistance How far in units of meters from the point of firing does the other fragment hit the ground if the terrain is level O 19 60 O 14 00 O 32 67 O 49 01 0 2450

8 Wind with a velocity 100 km h blows normally against one of the walls of a house with an area of 108 m Calculate the force exerted on the wall if the air moves parallel to the wall after striking it and has a density of 1 2 kg m ANSWERS 1 a Force will be along x direction on the wall 2my 1 b 2mv cos cos 2 8 10 Ns 2s 5 a 12 Ns b 4 8 ms c 2 8 ms d 2 40 N 3 0 75 Ns 7 5 N 4 150 3N

13 The velocity time graph for a moving body is shown in figure below If body moves in straight line along x axis without changing its direction then total displacement of body would be V 2 1 15 m O 12 m 1 2 3 4 2 10 m 4 Zero t

at the foot of the 10 A large heavy box is sliding without friction down a smooth plane of inclination 0 From a point P on the bottom of the box a particle is projected inside the box The initial speed of the particle with respect to the box is u and the direction of projection makes an angle a with the bottom as seen by an observer inside the box as shown in figure Pla 0 a Find the distance along the bottom of the box between the point of projection P and the point Q where the particle lands Assume that the particle does not hit any other surface of the box Neglect air resistance b If the horizontal displacement of the particle as seen by an observer on the ground is zerc find the speed of the box with respect to the ground at the instant when particle was projected

39 A car starts from rest accelerates on a straight path with constant acceleration a for some time after which it decelerates at constant value b and comes to rest Total time elapsed is t then average velocity of the car is 1 2 3 abt a b abt 2 a b 4 2abt a b a t a b AA

A force F power of F is P constant is applied on block A of mass m as shown in figure F is parallel to the inclined plane Then Smooth The maximum speed of block A is The maximum speed of block A is P mg sin e P mg cos e The speed of block A first increases and then becomes nearly constant Speed of block A continuously increases A m 0 F Fixed