Kinematics Questions and Answers

5 Two particles are projected simultaneously with same initial velocity u at angles 0 and respect to the horizontal but in opposite direction their paths are coplanar what is the magnitude of relative velocity at the time of projection 0

P 0 A B t 7 Fig 3 19 A woman starts from her home at 9 00 am walks with a speed of 5 km h 1 on a straight road up to her office 2 5 km away stays at the office up to 5 00 pm and returns home by an auto with a speed of 25 km h 1 Choose suitable scales and plot the x t graph of her motion A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward followed again by 5 steps forward and 3 steps backward and so on Each step is m long and requires 1 s Plot the x t graph of his motion Determine graphicall long the drunkard to

The maximum range of a bullet fired from a toy pistol mounted on a car at rest Ro will the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity v 40 m What 20 m s on a horizontal surface g 10 m s 1 30 3 75 2 60 4 45 2013

17 The distance travelled by a particle starting from 4 rest and moving with an acceleration ms 2 in the 3 third second is 1 6 m 3 10 C m 2 4 m 4 19 3 m

A body is projected vertically upwards If t and t2 be times at which it is at height h above the point of project while ascending and descending respectively then h is 1 1 2 3 2g t t 2 gt t 4 4g tit 66

7 A spy report about a suspected car reads as follows The car moved 2 00 km towards east made a perpendicular left turn ran for 500 m made a perpendicular right turn ran for 4 00 km and stopped Find the displacement of the car

If initial velocity of particle is 2 m s the maximum velocity of particle from t 0 to t 20 sec is A 20 m s 4 2 41 B 18 m s 8 10 12 16 20 C 22 m s D 24 m s

A bus starting from rest attains a velocity 72 km p h in 5 minutes acceleration is uniform its acceleration is in m s A 1 30 B 1 15 C 0 24 D 1 5

Position path length Instantaneous velocity and Instantaneous speed A person moves 30 m north then 20 m east and then 30 2 m south west His displacement from the origin position is 1 14 m south west 3 10 m west 2 28 m south 4 15 m east 1000 m It covers the first half of the distance at speed 40 km h and second half

Two particles A and B start from the same point and move in the positive x direction In a time interval of 2 00 s after they start their velocities v vary with time t as shown in the following figures What is the maximum separation between the particles during this interval v m s 2 00 1 00 2 00 v m s 1 00 1 1 00 m Particle A 1 00 Particle B 1 00 2 00 s t s 2 1 25 m 2 00

14 Raindrops are falling vertically with a velocity of 10m s To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of 20m s The velocity of cyclist is a 10 m s c 20 m s WM b 10 3 m s and ar to d 20 3 m s TUNS

This section contains 3 questions Each question contains statements given in two columns which have to be matched The statements in Column I are labelled A B C and D while the statements in Column II are labelled p q r s and t Any given statement in Column I can have correct matching with One OR More statement s in Column II 1 Two trains each of length 100 m are moving with speeds 54 km h for Train 1 and 90 km h for Train 2 on two parallel tracks Match the entries given in column I with the entries given in column II Column I Column II A Time taken in passing each other in s B Distance travelled by 1st train during passing in m C Distance travelled by 2nd train during passing in m if both trains are moving in same direction D Displacement of 1st train w r t 2nd train in 2 s in m 125 500 p q r 20 s 300 t 5

1 The wind is blowing from south at 10 m but to a cyclist it appears blowing from east at 10 ms The velocity of cyclist is towards S W towards N W 1 10 2 ms 2 10 2 ms towards S E 3 10 2 ms 4 10 2 ms towards N E

A B C and Dare points in a vertical line such that AB BC CD If a body falls from rest from A then the times of descend through AB BC and CD are in the ratio A 1 2 3 C 3 1 2 A particle is protected vertically unune B 2 3 1 D 1 2 1 3 2

A car starts from rest again comes to rest after travelling 200 m in a straight line If its acceleration and are limited to 10 m s 20 m s2 respectively then minimum time the car will take to travel the deacceleration distance is 1 20 s 2 10 s V 0 3 2 15 s 20 4 S 3

apns 35 The acceleration time graph of a particle is as shown At what time the particle acquires its initial velocity 1 12 s 3 85 a m s 10 O 4 2 5 s 4 16 s t s

10 The displacement of a particle is given by y a bt ct The initial velocity and acceleration are respectively 1 b 0 3 b 2c 2 b 2c 4 2c 4d

me graph of a particle of mass 2 kg moving along x axis is as shown in the figure The magnitude of impulse on the particle at t 2 s is NCERT Pg 110 x m 20 2 4 t s O OC M

All the graphs below are intended to represent the same motion One of them does it incorre JEE Ma it up 1 3 distance velocity time time 2 position 4 time velocity Br position

7 A particle is at rest at t 0 If acceleration of the particle is given as a sinnt cosnt in SI units then the maximum speed of particle is 1 3 2 NIK I m s TO 2 1 m s 2 2 2 TU 4 2 TU m s m s

A body falling freely from a given height H hits an inclined plane in its path at a height h As a result of this impact the direction of the velocity of the body becomes horizontal For what value of h H the body will take maximum time to reach the ground A1 1 B 2 4 D

P M A particle of mass 2 kg moves on a circular path with constant speed 10 m s Find change in speed and magnitude of change in velocity When particle completes half revolution The distance travelled by a particle in time t is given by s 2 5 t m Find a the average speed of the particle during time 0 to 5 0s and b the instantaneous speed at t 5 0 s A particle gogs from

unacademy Rain drops are falling with a velocity 10 2m sec making an angle of 45 with vertical The drops appear to be falling vertically to a man running with constant velocity The velocity of rain drops change such that the rain drops appear to be falling vertically with 3 times the velocity it appeared earlier to the same person running with same velocity The magnitude of velocity of man w r t ground is A 10 2 m s B 10 3 m s C 10m s D 20 m s

A ball is projected with velocity 5 m s at an angle of 60 with horizontal from ground The speed of the ball at the instant when its velocity is perpendicular to its initial direction of motion is g 10 m s 5 1 m s 3 3 5 2 m s 2 5 m s 4 10 m s

4 Two wires A and B are made of same material The wire A has a length 1 and diameter r while the wire B has a length 21 and diameter r 2 If the two wires are stretched by the same force the elongation in A divided by the elongation in B is a 1 8 b 1 4 c 4 d 8 c d 12 An a

4 Two motorboats that can move with velocities 4 0 m s and 6 0 m s relative to water are going up stream in a river When the faster boat overtakes the slower boat a buoy is dropped from the slower boat After lapse of a time interval 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 in the river is 1 5 m s find distance between the places where the faster boat passes by the buoy a 75 m c 300 m b 150 m d 350 m

Two identical balls are interconnected with a massless and inextensible thread The system gravity free space with the thread just taut Each ball is imparted a velocity v one towards the ball and the other perpendicular to the first at t 0 Then A the thread will become taut at t L v B the thread will become taut at some time t L v C the thread will always remain taut for t L v D the kinetic energy of the system will always remain mv

A particle moves along a straight line OX At a time t in seconds the distance x in metres of the particle from O is given by x 40 12t t How long would the particle travel before coming to rest 1 24m 2 40m 356m 4 16m

Three elephants A B and C are moving along a straight line with constant speed in same direction as shown in figure Speed of A is 5 m s and speed of C is 10 m s Initially separation between A B is d and between B C is also d When B catches C separation between A C becomes 3d Then the speed of B will be 1 7 5 m s 5m s 2 15 m s d 10m s 3 20 m s 4 5 m s

A train takes t sec to perform a journey It travels for 9 Se n sec with uniform acceleration then for n 3 sec with uniform speed v and finally it comes to rest with uniform retardation The n average speed of the train is

A projectile is projected with speed 60 m s at an angle 60 from the horizontal After some time projectile is moving at angle 30 with horizontal wha is value of 1 1 m s 5 3 m s 3 V at this instant Given g 10 m s 2 5 3 m s 4 5 m s

During the downward motion of an oblique projectile from top point of its trajectory the radius a curvature of its trajectory will 1 Remain constant 2 Increase 3 Decrease r decreass

02 A sports car is moving with constant speed 20 m s on a horizontal road Its motion is recorded by a camera which is at 40 m from the road as shown In order to focus the car camera is to be rotated at angular speed equal to 20 m s 1 40 m 1 000 rad s 45 Camera 500 rad s

5 3 There is an inclined surface of inclination 0 30 A smooth groove is cut into it forming angle a with AB A steel ball is free to slide along the groove If the ball is released from the point O at top end of the groove the speed when it comes to A is g 10 m s 1 40m s A Fixed 0 90 4m B 3m 2 20 m s 3 10 m s 4 15 m s

TOTAL 120 Motion in one dimension 12 A car travels a distance of 2000 m If the first half distance is covered at 40 km hour and the second half with speed u and the av speed is 48 km hour then the value of u is Clan hour b 60 km hour c 50 km hour d 48 km hour ting point in the next three hours Its a

A tennis ball treated as hollow spherical shell starting from O rolls down a hill At point A the ball becomes air borne leaving at an angle 300 with the horizontal The ball strikes the ground at B What is the value of distance AB Moment of inertia of spherical shell of mass m and radius R about its diameter 2 3 mR 1 1 87 m 3 1 57 m 2 2 08 m 4 1 77 m 2 0 m V0 2 m 130

A man is holding an umbrella at angle 30 with vertical with lower end towards himself which is appropriate angle to protect him from rain for his horizontal velocity 10 m s Then which of the following will be true 1 rain is falling at angle 30 with vertical towards the man 2 rain may be falling at angle 30 with vertical away from the man 3 rain is falling vertically

particle an angle with the horizontal into a uniform gravitational field The slope of the trajectory varies with horizontal distance x as Slope A 1 2 3 4 N y Slope Slope 4 Slope 4 TO X X X iDiff X ante Fzgj gxr 2440

n m s The value of n is A stone is dropped from the top of a tower and travels 24 5 m in the last second of its journey The height of the tower is n m The value of n is acceleration

A particle travels 10m in first 5 seconds and 10m in next 3 seconds Assuming constant acceleration what is the distance travelled in next 2 second 1 8 3 m 2 9 3 m 3 10 3 m 4 None of these

1 Speed of a boat in still water is half of velocity of flow of water v At what angle boat should steer with direction of flow of water so that drift of boat is minimum 30 3 90 2 60 4 120

105 Two particles move from A to C and A to D on a circle of radius R and diameter AB If time taken by both particles are same then ratio of magnitudes of their average velocity is 1 2 3 3 A 30 60 D C B 2 2 3 4 13 0

Initial velocity of a projectile is given by 207 50 70k m s If acceleration due to gravity is g 10 k m s then the time after which projectile return to the same horizontal level is axis system is L 1 4 s 2 10 s

A man start from point P and goes 20 m due east then 5 m due North then 35 m due west and finally 25 m due South His displacement from point P is 3 1 25 m at tan 4 2 85 m at South West 3 25 m at tan JAY 25 25 m at tan 3 4 3 South of West South of West West of South

9 A projectile is projected at an angle of bl horizontal At an instant it is moving at an angle of 30 with horizontal with velocity 10 m s The radial acceleration of particle at that instant is 2 20 2 m s 1 3 L 10 2 m s 3 4 5 5 m s 2

2 A body starting from rest is moving under a constan acceleration up to 20 sec If it moves S distance in first 10 sec and S distance in next 10 sec then S will be equal to 1 S 3 35 2 2S 4 45

velocity on a straight line path tangential to the earth s surface Another body B is thrown vertically upwards it goes to a height and falls back on earth A third body C is projected to an angle and follows a parabolic path as shown in figure MP PMT 2009 B a B only c A B C d The bodies whose angular momentum relative to the center of the earth is conserved are A earth b B and C d None of the above

36 A particle is moving in a circle of radius r with speed v as shown in the figure The magnitude of change in velocity in moving from P to Q is 1 2 v cos 40 2 2 v sin 20 40 r P 3 2 v cos 20 4 none of these overed in the nth

A person who can swim with spee water wants to cross a river of width d and water is flowing with speed v Minimum time in which the person can do so i 2 Jilly Mistake l 1 V d 3 2 2 2 u d

2 o rabbits wo trees e velocity e velocity 7 8 velocity m s 10 5 0k time s 1 2 3 4 5 6 The above graph represents the velocity of a lift going upwards starting from ground The lift reaches the height 1 30 m 2 20 m 3 40 m 4 60 m