Kinematics Questions and Answers

I block of mass m held compressed against a spring as shown in the figure The spring has force constant of k such that mg k 3m After releasing the block it collides a spheres of same mass which is suspended from a massless rod of length 3m The rod can freely rotated in a vertical circle about its top point Considering the coefficient of restitution 0 5 find the minimum compression in the spring so that sphere can complete full circle m

15 B A stationary boy is pulling the rope with speed 3v If velocity of bracket is v Find velocity of block B and time it takes in reaching pulley

small ball is thrown from foot of a wall with the minimum possible ocity to hit a bulb B on the ground a distance L away from the wall d expression for height h of shadow of the ball on the wall as ction of time t Acceleration due to gravity is g y 4 h

particle is moving with velocity v K y here K is a constant The general equation fo th is AIEEE 20 y x constant y x constant y x constant

6 1 The velocity of a train increases at a constant rate a from 0 to V and then remains constant for some time interval and then finally decreases to zero at a constant rate B If the total distance covered by the particle be x then the total time taken will be 1 3 2 1 1 B 1 NOUN 2 a B 2 V a 2a B 4 a 2a B

The states of motion and rest are relative Explain

b it re all through c at the instant just after the body is projected d at the highest position of the body 3 A stone falls freely from rest from a height hand it travels a 9h distance in the last second The value of his 25 a 145 m c 122 5 m e 175 m arth b 100 m Kerala CEE 2011 d 200 m horn of mass M and radius R The ho earth s

4 A boy throws a stone so as to hit a bird sitting on a wall 10 m high Just on throwing the stone the bird flies away horizontally with a velocity of 5 m s The stone further goes up to a maximum height of 20 m above the ground and then hits the bird Find the initial 5 17 ms tan 4 velocity of stone and its angle of projection

18 An object having a velocity 4 0 m s is accelerated at t rate of 1 2 m s for 5 0 s Find the distance travell during the period of acceleration

8 Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x t at bt2 and x ft t At what time do the cars have the same velocity 1 a f 1 b a f 3 2 b 1 2 4 f a 2 b 1 f a 2 b 1 v vtal 2

62 A particle is dropped from a height of 80 m and the of restitution of its collision with the coefficient 1 ground is e 2 covered by the particle before it finally stops 1 400 m 3 1600 3 Calculate the total distance 2 4 400 3 200 3

km De A body is projected vertically upward direction from the surface of earth If upward direction is taken as positive then acceleration of body during its upward and downward journey are respectively 1 Positive negative 2 Negative negative 3 Positive positive 4 Negative positive

A horse pulls a wagon of 3075 kg from rest against a constant resistance of 90 N The pull exerted initially is 600 N and it decreases uniformly with the distance covered to 400 N at a distance of 15 m from start Find the velocity in m s of wagon at this point

A ball is thrown vertically downward with a velocity of 20 m s from the top of a tower It hita the ground after some time with a velocity of 80 m s The height of the tower is g 10 m s 1 320 m 2 300 m 360 m 340 m

A ball is thrown from the ground with velocity u at an angle with horizontal The horizontal range of the ball on the ground is R If the coefficient of restitution is e then the horizontal range after the collision is 1 e R 3 eR 2 e R R

21 The motion of a particle is described by x xo 1 e kt t 0 xo 0 k 0 With what velocity does the particle start b xok a 71 xo k c k xo S d 2x k

EXAMPLE 20 Two particles P and Q move in a straight line AB The particle P starts from A in the direction AB with velocity u and acceleration f and at the same time particle Q starts from B in the direction of BA with velocity u2 and acceleration f2 If they pass one another at the middle point of AB and arrive at the other end of AB with equal velocities prove that U U f1 f2 8 f1 42 f2 41

velocity u Retardation acting on the particle is AV where k is a positive constant and v is stantaneous velocity Then 2 n 1 e okt 3 Displacement of partinic at time i is 4 Displacement of particle when it comes to rest

A boy standing on a horizontally moving platform throws a ball at some angle to the direction of motion of the platform Velocity of ball and platform are in same vertical plane To a man standing on ground the trajectory of the ball may be A ellipse B hyperbola C straight line D circle

rest Calculate the magnitude of average velocity of the Two particles move in concentric circles of radii r and r such that they maintain a straight line the centre Find the ratio of their angular velocities order to have samo

wave pulse on a string has the dimension shown in figure The waves speed is v 1 cm s If point O free end The shape of wave at time t 3 s is 0 2 1 cm 1cm 1 cm v 1cm s l m l m 3 2cm 0 1 cm D 1 cm 1 cm 2cm

with horizontal and strike at the same point in the horizontal plane through a point of projection If t and t are their time of flights 67 Then 1 3 17 27 1 2 t 1 3 tan tan a a 1 sin sin a a 66 If v and v be the velocities at the end of focal chord of projectile path and u is the velocity at the vertex of the path then 1 v v u 1 1 1 1 v v 2 4 u V V If a stone is to hit at a point which is at a distance d ways and at a height h see fig above the point from where the stone starts then what is the value of initial speed u if the stone is launched at an angle e d V V u 2 g sin a a sin sin 4 sin 2 verstand 1 2

An aeroplane moves with constant velocity v parallel to x axis at a height y h Find the a angular velocity b angular acceleration of the aeroplane relative to O as the function of time t Assume that at t 0 x 0 igita h

stration 11 A box of mass m 10 kg is projected up an inclined plane from its foot with a speed of 20 m s as shown in the figure The coefficient of friction u between the box and the plane is 0 5 Find the distance travelled by the box on the plane before it stops for the first time 20 m s 37 ve od

7 A motorcycle and a car start from rest from the same place at the same time and travel in the same direction The motorcycle accelerates at 1 0 m s 2 up to a speed of 36 km h and the car at 0 5 m s 2 up to a speed of 54 km h The time at which the car would overtake the motorcycle is a 20 s b 25 s c 30 s d 35 s

A lift is moving in upward direction with speed 20 m s and having acceleration 5 m s in downward directi A bolt drops from the ceiling of lift at that moment Just after the drop the A velocity of bolt with respect to ground is zero B velocity of bolt with respect to ground is 20 m s in upward direction C acceleration of bolt with respect to ground is 5 m s D none of these

A particle moving with a constant acceleration describes in the last second of its motion 9 25th of the whole distance If it starts from rest how long is the particle in motion and through what distance does it move if it describes 6 cm in the first sec 1 5 s 150 cm 3 15 100 co 2 10 s 150 cm 4 None 115

In the figure shown find out the value of 0 assume string to be fight A tam 3 4 B tan 4 3 10am s 15m s 45 10m s C tar 38 D Non

If R is the range of a projectile on a horizontal plane and h its maximum height then maximum horizc range with the same speed of projection is A 2h B R 8h C 2R h 8R D 2h R 8h

23 O A car starting from rest moves along a straight line with a constant acceleration The variation of speed v with distance s is given by 360 1 2 1630 29 3 4 S 2

The moment of inertia in rotational motio equivalent to 1 angular velocity of linear motion 2 mass of linear motion 3 frequency of linear motion 4 current Four point masses each of mass m are a in the X Y plane the moment of inertia of

5 A boat having a speed of 5 km hr in sti water crosses a river of width 1 km along th shortest possible path in 15 minutes Th speed of the river in Km hr A 1 C 4 B 3 D 41

4 A body of mass 1 kg is projected with velocity 50 m s at an angle of 30 with the horizontal At the highest point of its path a force of 10 N acts on body for 5 s vertically upward besides gravitational force What is the horizontal range of the body g 10 m s 14 a 125 3 m c 500 m b 200 3 m d 250 3 m

A cylinder of mass m 3 kg and radius R 2 m is attached to a massless spring pulley system as shown in the figure and all the springs are in their natural length at t 0 The friction is sufficient to cause pure rolling of the cylinder The time period of cylinder for small horizontal displacement is n n 6 then find the value n spring constant k 2 2 N m wwwwww ellele 4k monoicer cylinder 0 k

1 A point moves in the x y plane according to the law x a sinot y a 1 cosot Find the distance travelled by particle in first to seconds x a sinot ay a 1 cosot 3 D V x to acto

A body is projected at time t 0 from a certain point on a planet s surface with a certain velocity at certain angle with the planet s surface assumed horizontal The horizontal and vertical displacements y in meter respectively vary with time t in second as x 10 3 t and y 10 t t Then the maxim height attained by the body is A 200 m An obiect in th B 100 m C 50 m D 25 m

96 A particle is moving along positive x axis with Some initial velocity The acceleration time graphs are shown In which case velocity of particle will increased for entire time between 1 to 1 1 1 1 1 Only in II 3 In I and II 4 b 11 2 In I and II 4 In I II and III

An engine approaches a hill with a constant speed When it is at a distance of 0 9 km it blows a whistle whose echo is heard by the driver after 5 s If the speed of sound in air is 330 m s the speed of the engine is a 30 m sl c 32 mal b 60 m s

Two particle A and B are projected simultaneously from a fixed point on the ground Particle A is projected 2v on a smooth horizontal surface with speed v while particle B is projected in air with speed B hits the particle A the angle of projection of B with the vertical is A 30 B 60 C 45 D both A and B If particle

A ball of mass m is moving with speed y makes 2 perfectly elastic head on collision with a stationary ball of same mass They are in contact for very small time interval At The contact force between them varies as shown in graph Magnitude of F At my will be max Fmax F X3 At 3 Im 2X At f 1 wak fat

5v V 4 3v 2v A motor vehicle travelled the first third of a distances at a speed of V 10 kmph the second third at a speed of v 20 kmph and the last third at a speed of v 60 kmph Determine the mean speed of the vehicle over the entire distance s 3 2v V2 V V 1 15 kmph 3 10 kmph A motorist 2 12 kmph 4 18 kmph aco

71 A small stone is released from rest from the top of a multi storey building During its free fall the ratio of the distances moved by it during 1st 2nd and 3rd second of its journey will be 1 1 2 3 2 1 3 5 4 1 1 1 101 12 22 32

Hailstones falling vertically with speed of 10 m s hit with respect to himself the windscreen of a moving car and rebound elastically Find the velocity of the car if the driver find the hailstones rebound vertically after striking Windscreen makes an angle 30 with the horizontal

4 all the above are true 28 Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x t at bt and x ft t At what time do the cars have the same velocity a f 1 b 1 3 a f 2 b 1 f a 2 b 1 f a 2 b 1 2 4 speed ground si from wh 1 g 3 G A 34 A bod ration distar 1 73 3

A particle of mass 0 5 kg is moving in circular path of radius 1 m with constant speed 10 m s The magnitude of average force when particle travels from A to B will be 1 3 3v 2 r 3v B 3 2 4 A 12 2 r 6v

5 Find the resultant of the three vectors OA OB and OC shown in figure 2 W4 Radius of the circle is R C B 45 C 45 Figure 2 W4

3 8s 4 10 s A particle is projected vertically upwards with a velocity of 40 ms 1 Find the displacement of the particle in 8s 1 80 m 2 160 m 25 The slope of position time graph 3 0 m A 2 4 240 m nu sons en 29

Two trains A and B each of length 400 m and moving with a velocity of 72 km h are running on parallel tracks such that A is ahead of B initially Now the driver of the train B decided to overtake the train A and began to drive with an acceleration of 1 m s 2 The guard of B crosses the driver of A after 50 s What had been the initial distance between the two trains NCERT 1250 m

86 A particle of mass m is thrown at t 0 with kinetic energy K at an angle 30 with the horizontal from the top of a tower of height 80 m The particle again has kinetic energy K after time to The to is equal to 1 2Ko mg Ko 3 2mg 2 4 Ko mg Ko V4mg

30 The displacement of a particle as a function of time is shown in the figure The figure shows that Displacement 2 01 234 Time in second 1 The particle starts with certain velocity but the motion is retarded and finally the particle stops 2 The velocity of the particle is constant throughout 3 The acceleration of the particle is constant throughout 4 The particle starts with constant velocity then motion is accelerated and finally the particle moves with another constant velocity