Kinematics Questions and Answers

The velocity time graph of a particle moving in a straight line is given in the following figure Which of the following is incorrect v m s 15 10 5 4 t s 8 12 16 20 acceleration of particle at t 9sec is 2 acceleration of particle at t 16 sec is 5 displacement during first 10 sec is 135 m O displacement during first 10 sec is 105

Q 18 A particle is projected from a point A with velocity u 2 at an angle of 45 with horizontal as shown in figure It strikes the plane BC at right angles The velocity of the particle at the time of collision is a 3u 2 45 u 2 B 60 b c 2u d u

11 The relation between time t and distance x is t ax bx where a and bconstants are The acceleration is a 2aby b 2 bv c 2av d 2av fonward half a revolution on a horizontal ground The magnitude of

Q 13 A particle is projected with velocity vo along x axis The deceleration on the particle is proportional to the square of the distance from the origin i e a ax The distance at which the particle stops is a LALL 3V0 2 300 b b 2a hullet in firod at a target its velocity decreases by half after penetration 30 cm into it c 3v 2 3 v d

Ju Pt on increasing on increasing e acceleration 3 DUAL CAMERA Shot by Soundeen Monna CRE x Incass 0 0 goes on decreasing v goes on decreasing Negative acceleration 4 Displacement area under graph VA Disive t of 6 Velocity decreases Inceesset 0 90 ince inc B Fight pak LANCERFON

The displacement x of a particle varies with time t x ae a be t where a b a and are at positive constants The velocity of the particle will a Go on decreasing with time c Drop to zero when a B b Be independent of a and d Go on increasing with time

Q 25 A boy begins to walk eastward along a street infront of his house and the graph of his displacement from home is shown in the following figure His average speed for in the whole time interval is equal to a 8 mmin 1 Distance east metre 40 20 5 Time min b 6 mmin 1 10 15 20 8 c mmin 1 d 2 mmin 1

Q 22 A particle A is projected from the ground with an initial velocity of 10 ms at an angle of 60 with horizontal From what height h should an another particle B be projected horizontally with velocity 5ms so that both the particles collide in ground at point C if both are projected simultaneously g 10 ms B a 10 m 10 ms Har 60 b 30 m 5 ms c 15 m d 25 m

If the percentage error in the measurements of mass and velocity of body are 4 and 5 respectively then the maximum percentage error in the measurement of momentum of the body is 1 4 2 9 3 1 4 5

When you start your stopwatch a particle moving on the x axis is observed somewhere between the positions x 10 m and x 12 m Sometime during the fourth second it passes the position x 22 m and at the instant t 12 s it is observed somewhere between the positions x 55 m and x 60 m When do you expect its arrival at the position x 88 m

Question A body is thrown vertically upwards with a velocity u Select the incorrect statements from the following 1 Both velocity and acceleration are zero at its highest point II Velocity is maximum and acceleration is zero at the highest point III Velocity is maximum and acceleration is g downwards at its highest point O O O O I and III II and III I and II I II and III

17 The displacement x of a particle varies with time t x ae at be t where a b a and are positive constants The velocity of the particle will a Go on decreasing with time c Drop to zero when a B b Be independent of a and B d Go on increasing with time

Question A body is thrown vertically upwards If air resistance is to be taken into account then the time during which the body rises is O O O O less than the time of fall greater than the time of fall twice the time of fall equal to the time of fall

Two identical uniform spheres of mass M are at rest and another uniform sphere of mass m is moving along their lines of centers between them with speed u After second collision middle sphere move with velocity 0 36u If spheres are perfectly elastic then calculate M u M m

Question Two balls A and B of same mass are thrown from the top of the building A thrown upward with velocity v and B thrown down with velocity v then O O O C velocity A is more than B at the ground velocity of B is more than A at the ground velocity A is more than B at the ground

Q 10 A boat is sent across a river with a velocity of boat is 10 km hr If the resultant velocity of boat is 10 km hr then velocity of the river is a 10 km hr b 8 km hr c 6 km hr d 4 km hr where and hoonstants are The

35 A prism of mass M with its smooth inclined face inclined at an angle with the horizontal is kept on a rough surface A body of mass m is coming down the inclined face Which of the followin are correct A The acceleration of the body along the inlcined plane is g sin BY TH The frictional force fis 1 mg sin 20 The maximum frictional force is mg 2 D The frictional force f will be maximum when 45 M

A train is initially at rest on a straight track It then accelerates at a constant rate of 0 0887 m s for a time of 50 0 s It then accelerates at a rate of 1 81 m s2 for a further 20 0 s What distance did the train move in this total time in units of meters

A balloon starts rising from the ground with an acceleration of 1 25 m s after 8s a stone released from the balloon The stone will g 10 m s a Reach the ground in 4 second b Begin to move down after being released c Have a displacement of 50 m d Cover a distance of 40 m in reaching the ground

13 A particle of mass 2 kg starts motion at time t 0 under the action of variable force F 4t where Fis in N and t is in s The work done by this force in first two second is 1 16 J 2 8 J 3 4 J F 4 8 ma s ya v sat

A string with constant tension T is deflected through an angl 200 by a smooth fixed pulley The force on the pulley is a 2T cos b T costo c 2T sin d Tsinfo

7 The blocks A and B are arranged as shown in the figure The pulley is frictionless The mass of 4 is 10 kg The coefficient of friction of 4 with the horizontal surface is 0 20 The minimum mass of B to start the motion will be 1 2 kg 2 0 2 kg 3 5 kg 4 10 kg 8 A On the horizontal surface of a truck u B 06 block of 10 A pe movi angle 1 tar 2 tar 3 sir 4 cos 11 A blo lift w wher Find block

A model rocket flies upward at constant acceleration starting from rest at time 0 00 s and undergoes a displacement of 17 5 m during its first 0 250 s of travel What was its speed at the time 0 250 s in units of m s

Question A man throws balls with same speed vertically upwards one after the other at an interval of 2 sec What should be the speed of throw so that more than two balls are in air at any time O O Only with speed 19 6 m s More than 19 6 m s At least 9 8 m s Any speed less then 19 6 m s

From a town cars start at regular intervals of 30 s and run towards another town with constant speed of 60 km h At some point of time all the cars simultaneously have to reduce speed to 40 km h due to bad weather condition What will be the time interval between arrivals of the cars at the second town during the bad weather a 20 s c 40 s b 30 s d 45 s

2 2 Trajectories of two projectiles are shown in the figure Let T and T be the time periods and u and u be their speeds of projection Then YA 1 T T 2 X 2 T T

Paragraph for question nos 2 to 4 To find the speed of a river s current a boatman decides to carry out the following experiment He drops a wooden bucket into the water and himself sets off downstream rowing along the flow of river After 40 min he reaches a point A 1 km from his starting point and turns back After travelling some distance upstream he picks up the bucket turns round again and rowing downstream once more reaches A for the second time 24 min later after picking the bucket Assuming that the speeds of both current and boat are constant and also that no time is wasted on turning round How long does the boatman spend on rowing upstream to meet the bucket A 24 min 3 B 40 min C 84 min D 16 min What is the speed of the current A 1 km hr 4 B km hr 3 What is the boat s speed relative to the water B 1 km hr A 1 2 km hr 3 C km hr 4 C 0 75 km hr 3 D km hr 10 D none of these 3 3

A pendulum is hanging from the ceiling of a cart which is moving down a smooth inclined plane as given in the figure The angle made by string with normal to the ceiling in equilibrium is 0 60 90 120 60

What is the meaning of velocity increasing li nearly and non linearly And how does it aff ect acceleration Does acceleration increas e linearly if velocity is increasing nonlinearly If yes explain

A body of mass 1 kg crosses a point O moving with velocity of 60 m s A force of 10 N opposite to velocity starts acting on the body at O The body will cross point O again in 0 12 s 06s 09s 015 s

A mass m 1 kg moving horizontally with velocity vo 2m sec collides inelastically with a pendulum of same mass Find the maximum change in potential energy in Joule of combined mass 4

Q15 NTA Test 13 Single Choice mat V Friction is absent everywhere and the threads spring and pulleys a small oscillations will be thongo wwwwwww mongo VA mathongo wuthongo are massless If ma mathongo mathongo ngo mathongo m B D m then the angular frequency of the system for mathon mathon nathongo mathongo mathonco matho mathongo

Two identical balls are projected one vertically up and other at an angle of 30 to the horizontal with same initial speed The potential energy at their highest point is in the ratio 02 1 03 4 06 1 C r

A projectile of mass m is thrown with velocity v making an angle of 30 with vertical Neglecting air resistance the magnitude of change in momentum between the starting point and at the maximum height is Options 1 mv 2 2 3mv 2 3 mv

An object A is kept fixed at the point x 3 m and y 1 25 m on a plank P raised above the ground At time t 0 the plank starts moving along the with an 1 5 m s At x direction acceleration 1 25 m 3 0 m the same instant a stone is projected from the origin with a velocity u as show A stationary person on the ground observes the stone hittin the object during its downward motion at an angle of 45 the horizontal All the motions are in x y plane Find u an the time after which the stone hits the objec

thermally insulated vessel IS heat insulating piston which can move in the vessel without fric The left part of the vessel contains one mole of an ideal monatomic and the right part is empty The piston is connected to the right wa the vessel through a spring whose length in free state is equal to length of the vessel Fig 64 Fig 64 Determine the heat capacity of the

3 A ball was thrown from height H and the ball hit the floor with velocity 10 i 1 after 1 5 sec of its projection Find initial speed of ball Lx H 1 10 5 m s 2 5 5 m s 3 15 m s 4 30 m s In the above question the angle of projection 0 is 1 0 tan V 10 1 1 3 2 2 0 tan 3 0 tan 2 4 0 tan 1 In the above question 18 the height H is 1 3 75 m 2 2 25 m 3 150 m 4 47

A physics teacher finds a scrap of paper on which one of his students has written the following equation 02 52 2 X 9 8 X x of which of the following problem would this equation be part of the correct solution 9 24 A Find the speed of an object 5 seconds after it was dropped from rest B Find the distance of an object has fallen 5 seconds after it was released from rest oth C Find the height from which a ball when released will strike the ground with a speed of 5 m s D Find the maximum height to which a ball will rise if it is thrown upward with an initial speed of 5 m s

Drops of water fall at regular intervals from the roof of a building of height h 16 m The first drop striking the ground at the same moment as the fifth drop is ready to leave from the roof Find the distance between the 3rd and 4th dro O O O 7m 9 m 3 m Clear Respon

they both started the race from the resting position the race started at 7 00 pm and the tortoise reached the d estination by 9 00 pm the average spe ed of the tortoise remained 85 km h w hen the race began both accelerated fo rward the hare accelerated uniformly a t a rate of 1 m s2 for 5 sec it then con tinued at a constant speed for 12 5 se c before getting tired and slowing dow n with constant acceleration coming to rest 85 meters from where they started the tortoise accelerated uniformly for t he entire distance finally catching the h are just as the hare comes to a stop answer the following question how fast is the hare going 2 4 seconds

A body of mass m moving with a velocity v along a frictionless horizontal track and an another body of mass m 2 moving with 2 v collides with first body elastically Final speed of the first body is 2v Question Type Single Correct Type 1 2 5v 3 V

SolveLancer Test Which of the statement is correct for the given s t sraph I From 0 to t velocity is in negative direction II From 0 to t velocity is in negative direction III acceleration is negative throughout the motion IV direction of velocity remains constant SolveLancer Test a I II III b II III IV c None are correct 2 t t

13 A ball is dropped from rest at a height h from the 9h ground If it travels a distance of 25 y second of motion then value of h is g 10 m s You 2 125 m 4 80 m 1 225 m 3 in its last 150 m

20 The diagram shows particles A and B of masses 0 2 kg and m kg respectively connected by a light inextensible string which passes over a fixed smooth peg The system is released from rest with B at a height of 0 25 m above the floor B descends hitting the floor 0 5 s later All resistances to motion may be ignored A 0 2 kg B m kg 0 25m 1 Find the acceleration of B as it descends ii Find the tension in the string while B is descending and find also the value of m iii When B hits the floor it comes to rest immediately and the string becomes slack Find the length time for which B remains at rest on the ground before being jerked into motion again

positive x axis The velocity of a particle moving along x axis is given as v x 5x 4 in m s where x denotes the x coordinate of the particle in metres Find the magnitude of acceleration of the particle when the velocit of particle is zero A 0 m s B 2 m s2 C 3 m s2 D None of these

The height and width of each step of a staircase are 10 cm and 20 cm respectively A ball rolls off the top of a stair with horizontal velocity V and hits the 4th step The magnitude of V is g 10ms 2 A 2ms 1 B 2 2ms 1 C 1 5 5ms 1 D 7 3ms

36 A balloon of mass m is descending down with an acceleration How much mass should be removed from it so that it starts moving up with same acceleration 1 2m 3 3 3m EN m 4 4 m 36 31 A CHARA at 1 2m 3 ch Joak 3 3m 2 4 EN 1 m

9 0 Paragraph for Question Nos 8 to 10 A physics tutor launches a home built model rocket straight up into the air At t 0 the rocket is at y 0 with V t 0 0 The acceleration of the rocket is given by g ag Bt40 t tb where t ag B 1 4 A V a 1 gt C V a 1 gt A V The expression for the velocity V t valid at all times in the interval 0 t t is 1 1 B V a 1 gt Bts 3 A at agt agt gt ay Bts is the time at which fuel burns out a is a positive dimensionless number 1 1 5 Bts g t to The expression for the velocity V t valid for the time interval t t is 1 B V g t t 4 B 5 at 1 D V a 1 gt Bts The time taken for rocket to reach its maximum height is C V g t t D V agt gt 1 at integrate ay g txg BX witt D at 1 2

4 For a projectile launched upwards from level ground with initial velocity u and angle of projection 30 with vertical height of projectile above ground will be greater than horizontal distance covered upto time h CENTERS MUMBAI DELHI AKOLA LUCKNOW NASHIK PUNE NAGPUR BOKARO DUBAI 2 11

A particle takes 9s and 4s respectively to reach foot of the building when projected vertically upwards and downwards respectively with same speed from top of the building How much time in s particle will take to reach foot of the building when it is dropped from top of the building WWW www MBAR www CERTINDAN M WEDNE BU THANK QU SAMANT www WIENTE PA 10 20 Albalklim JOHA 2007082 240701 36 744 7