Kinematics Questions and Answers

10 A particle acceleration Then starts from rest at x 0 and varies with x as shown in the figure a m s 4 0 20 x m 1 The particle comes to rest at x 20 m 2 Maximum velocity in positive x direction is 4 5 m s 3 Velocity at x 10 m is 60 m s 4 Distance covered by particle till it returns to initial position is 80 m

A car A leaves city x at t 0 and moves with constant speed 40 km h due West Another car B leavesh later from city y which is 30 km South West of x and moves with constant speed 20 2 km h North West Choose the correct option s Choose only 1 answer A B The minimum separation of cars is 20 km They are at minimum separation at

A pendulum suspended from the roof of an elevator at rest has a time period T when the elevator moves up with an acceleration a its time period becomes T when the elevator moves down with accleration a its time period becomes T3 then 1 T T T3 2 T T T TT 2 3 T T T

graph for a particle is shown in the figure then Velocity m s 15 m s 10 m s 5 m s 5 A B D C E 10 Time s 16 The distance and displacement of the particle from 0 to 15 seconds is 1 100 m 50 m 2 100 m 100 m 3 100 m 200 m 4 100 m 0 17 The distance and displacement of the particle between 10 s to 20 s is 1 50 m 100 m 2 50 m 0 3 50 m 50 m 4 100 m 50 m 18 In which time interval the particle is speeding up 1 0 to 10 s 2 10 to 15 s 3 15 to 20 s 4 10 to 20 s 9 In which time interval the particle is moving with zero acceleration 1 0 to 5 s 2 5 to 10 s 3 10 to 15 s 4 15 to 20 s O In which time interval the particle is moving with negative acceleration 1 5 to 10 s 2 10 to 15 s 3 15 to 20 s 4 0 to 5 s 15 20

A motorboat is racing towards north at 20 km h and water current in that region is 10 km h in a direction 60 east of south The resultant velocity of boat is 26 4 km h 17 3 km h 30 km h 23 9 km h

38 The ceiling of a hall is 40 m For maximum horizontal distance the angle at which the ball can be thrown with a speed of 56 ms without hitting the ceiling of the hall is Take g 9 8 ms a 60 c 45 K RIN b 30 d data insufficient

Smooth The block has uniform mass density The tension at mid point of the block is M 6 kg 5 m 6 N M 6 kg 8 N 14 N 12 N 20 N hr F 22 N E

A body with mass 5 kg is acted upon by a force F 31 41 N If its initial velocity at t 0 is v 61 12j ms then the time at which it will just have velocity along x axis is 12 s 14 s 10 s

8 Two particles A and B are in XOY plane initially at 3m 5m and 5m 3m velocities They started to move with velocities V 31 51 and m VA S Vg a 7 matt 0s respectively If particles S collides then find the value of a

A ball is dropped from a 45 m high tower while another is simultaneously thrown upward from the foot at 20 m s along the same vertical line If the collision is perfectly elastic first ball reaches ground after time

The velocity of a body as a function of time t is given as m s What is force acting on the body at t 2 v 2ti t j s if its mass is 4 kg 4i 7 N 121 18j N E 8i 16 N

42 A ball of mass mis thrown upward with a velocity v If air exerts an average resisting force F the velocity with which the ball returns to the thrower is mg Vmg F mg F mg F a v c v F Vmg F d None of these b v

points A particle moves along the x axis in such a way that its acceleration at time t for t 0 is given by a t 4 cos 2t At time t 0 the velocity of the particle is v 0 1 and its position is x 0 0 Find the position function x t

In a smooth stationary cart of length d a small block is projected from the rear end of the cart along it s length with velocity v towards front end Coefficient of restitution for each collision is e The cart rests on a smooth ground and can move freely The time taken by block to come to rest w r t cart is Assume the time for collision is negligibly small d ed 1 e v ed 1 e v V ho

At the initial moment three point A B and C are on a horizontal plane along a straight line such that AB BC Point A begins o move upward with a constant velocity v and point C downward without any initial velocity at a constant acceleration a If the points begin to move simultaneously then the initial velocity and acceleration of point B for all the three particles to be constantly on same straight line must be upwards downwards V a upwards upwards downwards downwards downwards upwards

A rain drop of mass 0 1 g is falling with uniform speed of 10 cm s What is the net weight of the drop g 10 m s A ON B 2 x 10 3 N C 10 N D 10 3 N The equation of state corresponding to 8 g of O2 assume ideal gas is

3 A particle is projected with a velocity of 10ms at an angle 37 with horizontal A bird moves along the path of projected particle with constant speed of 4 ms 1 Find the acceleration of bird when it is at highest point of path of particle g 10ms 2 a O zero b O 10 ms 2 c O 5 ms 2 d O 2 5 ms 2

0 Three points are located at the vertices of an equilateral triangle whose sides equals 2 3m They all start moving simultaneously with velocity v constant in modulus with the first point heading continually for the second the second for the third and the third for the first What will be the initial radius of curvature of the trajectory of each point in meters O 1 2 O 3 04 O 5 06 07 08 09

A truck with a wide load proceeding slowly along a secondary road approaching a tunnel that is shaped like a semicircle The maximum height of the tunnel is 5 25 m If the load is 8 m wide and 3 5 m high will it fit through the tunnel Show your calculations and explain you reasoning

8 A force F 21 53 k N is acting on a particle The particle is first displaced from 0 0 0 to 2m 2m 0 along the path x y and then from 2m 2m 0 to 2m 2m 2m along the path x 2 m y 2 m The total work done in the complete path is a 12 J c 16 J b 8 J d 10 J

A commander fires a shell at certain angle of projection from A which clears the building cuboid of dimensions 20 x 15 x 12 5 m in it s diagonal plane Shell just clears the roof diagonally at points P and Q and falls on the other side of the building at B and makes 45 angle with horizontal at P and Q as shown in the figure If the range AB of the shell is Nx 3 metre then find N g 10 m s A P450 15 m 20 m 12 5m B

A train starts from rest from a station with acceleration 0 2 m s on a straight track and then comes to rest after attaining maximum speed on another station due to retardation 0 4 m s If total time spent is half an hour then distance between two stations is Neglect length of train 1 216 km bhd 2 512 km d

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 crossi me 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

A length L 15 m of flexible tape is tightly wound It is then allowed to unwinding as it rolls down a fixed inline that makes angle 0 30 with the horizontal the upper end of the tape being fixed Find the time taken in second by the tape to unwind completely Neglect the radius at any time w r t the length of the rope 8

A person drops a cylindrical steel bar Y 5 00 10 0 Pa from a height of 4 70 m distance between the floor and the bottom of the vertically oriented bar The bar of length L 0 870 m radius R 0 00700 m and mass m 1 400 kg hits the floor and bounces up maintaining its vertical orientation Assuming that the collision with the floor is elastic and that no rotation occurs what is the maximum compression Al of the bar Use the gravitational acceleration g 9 81 m s

If x is horizontal and y is vertically upwards direction and the top of a tower 40 m high is taken as origin equation of trajectory of a projectile is y 40 x 4x Which of the following statement s is are true about the motion x y are in meters A Maximum height above ground is 100 m B Horizontal distance of the point where the projectile has same speed as at the time of projection is 10 m C Distance from the base of the tower where it strikes ground is more than 12 m D Minimum velocity of proiectile will be greater than 1 m s

rocket is launched from a tower The height of the rocket y in feet is related to the ime after launch x in seconds by the given equation Using this equation find the naximum height reached by the rocket to the nearest tenth of a foot y 16x 146x 137

A 20 kg block is in motion on a rough horizontal surface A horizontal force of 60 N is requited to keep the body moving with constant speed Then the coefficient of kinetic friction is 3 x 10 Find the value of x g 10 m s

To a stationary man rain is falling on his back with a velocity 6 km h at an angle 30 with vertical To make the rain velocity appear vertical the man should move 1 Forward with a velocity 3 km h 2 Forward with a velocity 3 3 km h 3 Backward with a velocity 3 km h 4 Forward with a velocity 2 3 km h

inst A monkey is sitting with a walnut at a tree of height H He drops it vertically by mistake and wants to catch the walnut at highest point of its trajectory after bouncing off the ground Calculate the minimum speed with which monkey should climb down if coefficient restitution of collision with ground is ea Hg a 1 e b 1 Hg c e Hg d e Hg

SolveLancer Test A monkey is sitting with a walnut at a tree of height H He drops it vertically by mistake and wants to catch the walnut at highest point of its trajectory after bouncing off the ground Calculate the minimum speed with which monkey should climb down if coefficient restitution of collision with ground is e SolveLancer Test a 1 e Hg b 1 Hg c 1 e Hg d e Hg

A person driving a car with a speed of 72 Km h observe a boy crossing the road at a distance of 100 m from car Driver apply the brake and retard the car with a retardation of 5 m s2 and just able to avoid the accident The reaction time of driver is 1 2 0 s 3 3 0 s 2 4 2 4 s 2 8 s

A point object O is placed in front of a concave mirror of focal length 20 cm on the principal axis of the concave mirror at a distance of 5 cm from the pole as shown in the figure A glass slab is also placed in front of the mirror perpendicular to this principal axis The image formed by the system for first reflection and then refraction is A virtual behind the mirror C virtual between the mirror and the slab P 1 5 cm 5 cm Li Glass slab B real between the mirror and the slab D can t be decided by above data

A boat capable of moving 6 5 m s is pointed at an angle upstream If the boat appears to moves directly north across the water what is the boat s ground velocity and the time it takes to cross the water Paragraph V The boat s ground velocity is BIU and the time it takes to cross the water is

39 A smooth square platform ABCD is moving towards right with a uniform speed u At what angle 9 must a particle be projected from A with speed u so that it strikes the point B B a sin c cos 4 A 0 C D b cos d sin 1

A parachutist drops freely from an aeroplane for 10 s before the parachute opens out Then he descends w 10 m s hit velo a net retardation of 2 5 m s2 If he bails out of the plane at a height of 2495 m and g on reaching the ground will be A 5 m s B 10 m s C 15 m s D 20 m s

A hollow massless sphere of radius R is fully filled with non viscous water of mass m It is rolled dow a horizontal plane such that its centre of mass moves with a velocity v If it purely rolls A Kinetic energy of the sphere is 1 2 mv B Kinetic energy of the sphere is 14 5mv C Angular momentum of the sphere about a fixed point on ground is mvR D Angular momentum of the sphere about a fixed point on ground is 14 5 mvR

3 A wooden block of mass m is pulled up an inclined plane having an inclination 0 with the horizontal with a force that makes an angle with plane as shown in the figure If the coefficient of kinetic fric tion between the plane and the block is uk derive an expression for the acceleration of the block F F 4

4 i A body is projected upwards with a velocity of 30 m s Find a the time when its velocity will be 5 m s b the time when it will be 20 metres above the point of projection and c the time when it will return to the point of projection 6 ii A stone is dropped from the top of a tower 60 m high Another stone is projected upwards at the same time from the foot of the tower and meets the first stone at a height of 18 m Find the velocity with which the second stone is projected upwards 4

5 i A particle starting from rest moves in a straight line whose equation of motion is given by s 3t 2t where s is in metres and t in seconds Find i velocity after 3 seconds ii acceleration at the end of 3 seconds and iii average velocity in the 4th seconds 4 ii A shot is fired with a velocity if 30 m s from a point 15 metres in front of a vertical wall 6 metres high Find the angle of projection to the horizontal for the shot just to clear thetop of the wall 6

ppose you throw a ball straight up from the ground with a velocity of 224 feet per second As the ball moves up gravity slows it Eventually the ball begins to fall back to the ground The heighth of the ball after t seconds in the air is given by the equation 16t2 224t Use the given information to answer parts a through c Find the height of the ball after four seconds ft

A body starting from rest moves with uniform acceleration on a horizontal surface The body covers 3 consecutive equal distances from beginning in time t t and t3 seconds The ratio of t t t3 is 1 1 2 3 3 2 1 2 3 1 2 1 3 2 4 3 2 1

11 A metal rod 1 8 m long increases in length by 1 4 mm when heated from 0 C to 50 C Find the coefficient of linear expansion of metal

8 00AM 1 00PM 1 00 PM 6 00PM 6 00PM 1 00AM 1 00AM 8 00AM NO LOAD This transformer has no load core loss of 270 watts and a full load ohmic loss of 12 65KW 35KVAR 80KW 50KVAR 30KW 30KVAR

A boy is driving a model aircraft with the help of a light inextensible cord of length L He does so by moving the free end of the cord with a constant speed in a horizontal circle of radius r As a result the aircraft moves in another horizontal circle of radius R r with a constant speed v at an altitude h above the plane containing circular path of the end held The centres of both the circular paths lie on a vertical line Considering the air drag find lift force of air on the aircraft

Example 5 5 Two identical billiard balls strike a rigid wall with the same speed but at different angles and get reflected without any change in speed as shown in Fig 5 6 What is i the direction of the force on the wall due to each ball ii the ratio of the magnitudes of impulses imparted to the balls by the wall U U X u u 30 0 30

mediately after the connection at B has been released Y 1 2 c Pin Supports B 1 2 c X Wires 1 ii The angular acceleration of the plate The acceleration of its center of mass B n 1 2 c b A www iii S

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 decreasing with time b increasing with time c constant but not zero d zero

A train starts from rest and accelerates uniformly at a rate of 2 m s 2 for 10 s It then maintains a constant speed for 200 s The brakes are then applied and the train is uniformly retarded and comes to rest in 50 s Find i the maximum velocity reached ii the retardation in the last 50 s iii the total distance travelled and iv the average velocity of the train Ans i 20 m s ii 0 4 m s 2 iii 4600 m iv 17 69 m s 1

In an I P L Chris Gayle of R C B hit a six which lands on the roof of Stadium situated at a distance of 60m from gayle If time of flight of ball is 4 sec and ball hits the stadium roof at an angle of 45 with horizontal in downward direction then C G 1 60m Initial speed of the ball when Gayle hit the ball was Question Type Single Correct Type 150 m s 45