Kinematics Questions and Answers

7 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 Q in 6 s Which of the following statements is not correct regarding the motion of the car 0 Q P 240 m 0 m 360 m A The average speed of the car in going from O to P and come back to Q is 20ms B The average velocity of the car in going from O to P and come back to Q is 15ms 1 A B are true 2 A B are false 3 A true B fasle 4 A false B true

The driver of a train moving at a velocity u finds a goods train ahead moving in the same direction at a velocity u u u at a distance x from his train and applies brakes producing a retardation a Prove that a collision can be avoided if x u 2a

36 Two balls are projected vertically upward direction with same speed 60 m s at an interval of 2 s The time from the projection of the second body after they will meet is take g 10 m s 1 5 s 2 6 s 3 7 s 4 8 s

0 A point has equal velocities in two given directions If one of these velocities is halved then the angle which the resultant makes with the other is also halved The angle between the velocities is 1 30 3 90 2 60 4 120 A is 17

tration 4 On an open ground a motorist follows a track that turns to his left by an angle of 60 after every 500 m Starting from a given turn specify the displacement of the motorist at the third sixth and eighth turn Compare the magnitude of displacement with the total path length covered by the motorist in each case com

7 A person standing on the top of a cliff 171 ft high has to throw a packet to his friend standing on the ground 228 ft horizontally away If he throws the packet directly aiming at the friend with a speed of 15 0 ft s how short will the packet fall

3 c d are correct 4 a d are correct 51 Velocity v versus displacement x plot of a body moving along a straight line is as shown in the graph The corresponding plot of acceleration a as a function of displacement x is 2014 E 1 Velocity 3 100 4 100 100 200 Displacement 200 x 200 2 X 4 a X 100 100 200 200 X X

8 An object may have a varying speed without having varying velocity b varying velocity without having varying speed c nonzero acceleration without having varying velocity d nonzero acceleration without having varying speed 1 a b c are correct 2 b d are correct 3 a b d are correct a d are correct

Topic 4 Motion Under Gravity 5 A stone falls freely under gravity It covers distances h h and h in the first 5 seconds the next 5 seconds and the next 5 seconds respectively The relation between h h and hz is 2013 a h h2 h3 3 5 b h 3h and h3 3h c h h h

1 73 cm s 2 80 cm s 3 85 cm s 4 90 cm s 15 A bullet fired into a fixed target loses half of its velocity in penetrating 15 cm How much further it will penetrate before coming to rest 1 5 cm 2 15 cm 3 7 5 cm 4 10 cm uniform accele

3 A man throws balls with the same speed vertically upwards one after the other at an interval of 2 second What should be the speed of the throw so that more than two balls are in the sky at any time Given g 9 8 m s 1 More than 19 6 m s 2 At least 9 8 m s 3 Any speed less than 19 6 m s 4 Only with speed 19 6 m s

A wheel is rolling straight on ground without slipping If the axis of the wheel has speed v the instantaneous velocity of a point P on the rim defined by angle 0 relative to the ground will be 1 U cos 3 v 1 sin 0 01 20 cos 10 4 v 1 cos 0 2 2u cos

The velocity v of a body moving along a straight line varies with time t as v 2t e t where v is in m s and t is in second The acceleration of body is zero at t da 1 O 3 3 2 2 s 4 Both 1 2

The x coordinate of a particle moving along x axis varies with speed v as x a bv The maximum possible speed of the particle is 1 3 2a b n 2 4 a a b

A ball is thrown up from the top of a tower with an initial velocity of 10 m s at an angle of 30 with F the horizontal It hits the ground at a distance of 173 m from the base of tower Calculate the height U of the fower g 10 m s h u sin 1 10m 2 10cm 3 100m 4 Im 29

3 4 none of these 10 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 Q P A B t 1 A lives closer to the school than B 2 A starts from the school earlier than B 3 A walks faster than B A and R ranch hom 15 16 17

g sin e Example 38 Two bodies are thrown simultaneously from he same point One thrown straight up and the other at an ngle a with the horizontal Both the bodies have velocity ual to u Find the separation between the bodies at time t tion YA y

3 The reaction time for an automobile driver is 0 7 sec If the automobile can be decelarated at 5 m s calculate the total distance travelled in coming to stop from an initial velocity of 8 33 m s after a signal is observed 1 12 77 m 2 14 82 m

3 11 2 x 7 4 7 11 2 11 Distance travelled by the tip of minute hand of length 10 cm in 100 sec is 1 3 T 180 m T 1200 m 2 4 TC 360 m 3 2160 m ZANODEO Z NODE02 8060 8A NURTURE PHYY

The displacemen shown in the figure Which of the velocity time graphs could represent the motion of the same body 3 1 404 30 20 10 Displacement 10 5 10 t Parabola 2 4 10 time s 5 10

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

9 With what speed should a body be thrown upwards so that the distances traversed in 5th second and 6th second are equal Take g 9 8 m s A 58 4 m s C 98 m s B 49 m s D 98 m s

3 3 The angle of projection when the range is equal to the distance through which the particle would have to fall in order to acquire a velocity equal to i velocity of projection 1 30 3 45 2 75 4 60

3 A cyclist moves in such a way that he takes 72 turn towards left after travelling 200 m in straight line What is the displacement when he just takes fourth turn 1 Zero 3 400 m 2 600 m 4 200 m tic

1 A retarding force F 2v is acting on a body of mass 10 gram Find out time taken for its velocity to reduce to 37 of its initial value if initial velocity is 1 m s 1 2 5 ms 3 75 mo 2 5 ms LAY O

A body of mass 3 0 kg starts from origin with an initial velocity 30 40 m s If a constant force 61 51 N acts on the body then the time in which x component of velocity becomes zero is M 1 15 s 3 24 s 48 2 5s 44 12a 4 30 s a 4

A ball which is thrown vertically upwards reaches the roof of a house 100 m high At the moment this ball is thrown vertically upward another ball is dropped from rest vertically downwards from the roof of the house At which height will the balls pass each other 121

For ground to ground projection following curves are given a D acceleration Horizontal disp Find incorrect one 2 b P 3 velocity in vertical dir vertical 5 dsip 4 d

mass 13 In the arrangement shown in Fig 6 193 a wedge of m3 Small and light pulley is connected on its top edge as 3 45 kg is placed on a smooth horizontal surface shown A light flexible thread passes over the pulley Two blocks having mass m 1 3 kg and m 1 5 kg are connected at the ends of the thread m3 m 37 Fig 6 293 inclined m is on smooth horizontal surface and m rests on smooth surface of the wedge The base length of wedge is 2 m and inclination is 37 m is initially edge of the wedge If the whole system is released from rest calculate a velocity of wedge when my reaches its bottom near the top

mmmm smooth surface Figure shows the displacement of a particle going along the X axis as a function of time The force acting on the particle is zero in the region A body of mass 45 kg is moving with a constant velocity of 10 m s A constant force acts on the body for 7 m r in opposite direction calculate the acceleration 12 The breaking str A for which the g 10m s

Consider the situation shown in the figure The horizontal surface below the bigger block is smooth The coefficient of friction between the blocks is u Find the minimum and the maximum force F that can be applied in order to keep the smaller blocks at rest with respect to the bigger block F A m Mass M C m B

A particle moves along a straight line with retardation a k k is a positive constant The velocity of the particle at time t 0 is u How far would the particle move before coming to rest How much time would it take 2 u 3 k

99 In the arrangement shown the motor at A is drawing the string with speed v The velocity of Mis 1 3 V M 2 4 AO V

A particle of mass m moves under the influence of the force F a sin ot i cos tj where a are constants and t is time The particle is initially at rest at the origin The instantaneous power given to the particle is A zero C a cos ot mo B a sin ot mo D a sin ot cos wt mo

32 The velocity time graph of a particle in one dimensional motion is shown in the figure Which of the following formulae is correct for describing the motion of the particle over the time interval t to t at 1 x 1 x t v t t 2 v t v t a t x t x t 3 Vaverage t 1 v t v t a t 1

B An electrical appliance having a resistance of 2002 is operated at 200 V Calculate the energy consumed by the appliance in 5 minutes in joule ii in Ans i 60 000 J ii 0 0167 kWh kWh

A particle moves along a straight line path After some time it comes to rest The motion is with constant acceleration whose direction with respect to the direction of velocity is a positive throughout motion b negative throughout motion c first positive then negative d first negative then positive

On a foggy day two drivers spot in front of each other when 80 metre apart They were travelling at 70 kmp follo 60 kmph following statements is correct 1 The collision will be averted 3 They will cross each other 2 The collision will take place 4 They will just collide

If the rate of change in velocity w r t time constant and its position after 6th second will be same as that after 11th second then the particl returns to the starting point at time t equals to 1 13 s 2 15 s 3 17 s

54 What should be the value of M so that the block does not slide over the triangular wedge All surfaces are smooth 3 m 1 3 1 m 2 4 3 1 m 5 3 1 2 5 5 1 LAY 4 m E m 30 M

The displacement x of a particle moving along x axis varies with time t as x 2 3 m where it is in seconds then 1 The particle returns to its initial position after s 2 The particle comes to rest at t s 3 Initial velocity of particle is zero day 200 4 Maximum velocity in positive x direction is 4 m s

A particle covers each 1 3 of the total distance with speed V V and V3 respectively Find the average speed of the particle A VV V V Vs V V 2V V V3 B VV VV V V C 3V V V V V V3 3V V V D VV V Vg VV

A shell projected vertically upward explodes into three identical fragments at the top of its flight After the explosion one fragment moves vertically downwards and hit the ground in time t while the other two hit the ground in time t2 Denoting acceleration due to gravity by g find the height above the ground where the shell exploded

Illustration 13 A 1 0 kg block collides with a horizontal light spring of force constant 2 N m The block compresses the spring 4m from the rest position Assuming that the coefficient of kinetic friction between the block and the horizontal surface is 0 25 what was the speed of the block at the instant of collision

Illustration 7 A man of mass m is standing on a stationary wooden board of mass M kept on smooth ice The man starts running on the board and acquires a speed u relative to the board Find the speed of the man relative to the stationary observer The board is long enough

spring Example 8 7 A block whose mass is 1 kg is fastened to a spring The spring has a s constant of 50 N m The block is pulled to a distance x 10 cm from its equilibrium position at x 0 on a frictionless surface from rest at t 0 Calculate the kinetic potential and total energies of the block when it is 5 cm away from the mean position

m n 1 A point moves in the plane so that its tangential acceleration w a and its normal acceleration w bt4 where a and b are positive constants and t is time At the moment t 0 the point was at rest Find how the curvature radius R of the point s trajectory and the total acceleration w depend on the distance covered s with rola ty whose

5 A man is standing on top of a building 100 m high He throws two balls vertically upwards one at t 0 and other after a time interval less than 2 s The later ball is thrown at a velocity of half the first The vertical gap between first and second ball is 15 m at t 2 s The gap is found to remain constant The velocities with which the balls were thrown are Take g 10 m s a 20 m s 10 m s c 16 m s 8 m s b d 10 m s 5 m s 30 m s 15 ms

Illustration 11 A bullet leaving the muzzie of a rifle barrel with a velocity v penetrates a plank and loses one fifth of its velocity It then strikes second plank which it just penetrates through Find the ratio of the thickness of the planks supposing average resistance to te penetration is same in both the cases

1 A football player kicks a ball at an angle of 37 to the horizontal with an initial speed of 15 ms Assuming that the ball travels in a vertical plane calculate i the time at which the ball reaches the highest point ii the maximum height reached iii the horizontal range of the projectile and iv the time for which the ball is in air Ans i 0 92 s ii 4 16 m iii 21 2 m iv 1 84 s