Kinematics Questions and Answers

Q2 P Q R 0 and P 3 Q P 9 between P and R is tan 1 143 3 153 4 and R 5 angle 13 3 37 4 2 37 4 53

Measure the time it takes you to walk from your house to your bus stop or the school If you consider that your average walking speed is 4 km h estimate the distance of the bus stop or school from your house

Drops of water are thrown tangentially off the horizontal rim of a rotating wet umbrella The rim is 3 ft in diameter and is held 4 ft above the ground and makes 14 revolutions in 33 seconds Drops of water will meet the ground on a circle of diameter in ft

10 Area under the curve y 3x between the ordinates x 0 to x 2 is 1 8 m 3 2 m 2 3 m 4 9 m

vectors 1 at sin at 4 B cos A sin at i cos at and are orthogonal to each other the value to t would be where a is positive constant 1 t 2 3 t 6 2 t 4 4 t 8

24 Three blocks P Q and R of masses 5 kg 4 kg and 3 kg respectively are connected by light inextensible string and they are moved on a smooth horizontal plane If a force of 24 M is applied to the string connected to R tensions T and T in the string are 1 1 20 N 5 N 3 10 N 18 N 5 kg P T 4 kg Q T 3 kg R 2 5 N 20 N 4 18 N 10 N 24 N

08 A body is projected vertically up at t 0 with a velocity of 98 m s Another body is projected from the same point with same velocity after 4 seconds Both bodies will meet at t 1 6 s 2 8s 3 10 s 4 12 s

A man running on a horizontal road at 8 ms finds rain falling vertically If he increases his speed to 12 ms he finds that drops make 30 angle with respect to the vertical Find the velocity of rain with respect to the road A 4 7 ms 1 8 2 ms 1 B C 7 3 ms 1 D 8ms 1

Figure shows the graph of velocity versus time for a particle going along x axis Initially at 0 particle is at x 3m Find position of particle at t 2s in m v m s t Ta boks 10 8 t s

43 A projectile is moving on xy plane such that horizontal and vertical direction are along x axis and y axis respectively The projectile is fired from the origin at a large height with initial velocity 50i 20 m s The time after which instantaneous velocity of the projectile becomes perpendicular to its initial velocity is 1 7 5 s 21 55 2 14 5 s 4 10 5 s

The potential energy of a particle of mass 1 kg along x axis is U 5 1 cos3x J The time perion of small oscillation is 1 2 5 3 5 2m 3 2 2 3 5 T 4 25

20 A particle starts from rest Its acceleration a versus time t is as shown in the figure The maximum speed of the particle will be a 110 m s c 550 m s 10 m s t s b 55 m s b 660 m s

A particle acceleration Then varies with x as shown in the figure a m s 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 particle oscillates along a straight line 1m long If it completes one oscillation in 0 1s find a the distance covered by it b its average speed and c its average velocity in one oscillation Ans 2 m 20 m s zero 1061 Find the overage time required by light to reach

35 From the board as shown a particle is thrown with a velocity V particle board 10j 20i The board is accelerating in the positive x direction at 10m s If after 1 sec the particle passes through the ring on the board then the value of the ratio H H is RING H 10m s

37 The x t graph shown in figure represents 20 Displacement Time 1 constant velocity 2 velocity of the body is continuously changing 3 instantaneous velocity 4 the body travels with constant speed up to time t and then stops

Take g 10 ms A body is dropped from a height of 2 m It penetrates into the sand on the ground through a distance of 10 cm before coming to rest What is the retardation of the body in the sand 100 okrat

3 A car moves from x to y with a uniform speed v and returns to y with a uniform speed v The average speed for this round trip is AIPMT Prelims 2007 1 2 Vu Vd 2 4 2v Vd Va Vu 3 VVd Va Vu d

Illustration 8 A gun is mounted on a stationary rail road car The mass of the car the gun the shells and the operator is 50 m where m is the mass of one shell Two shells are fired one after the other along same horizontal line in same direction If the muzzle velocity velocity with respect to gun of the shells is 200 m s then find the speed of the car after second shot

A rifle bullet loses 1 20th of its velocity in passing through a plank What will be the least number of such planks required to just stop the bullet

24 Figure shows the position time graph of a particle of mass 4 kg Let the force on the particle for t 0 0 t 4s t 4 s be F F and F3 respectively 1 2 Then a c x m A 3 F F F 0 3 F F F3 t s b F F F3 d F F F3

A stone is vertically projected up with a velocity of 25 m s Find its time of descent Take g 10 m s2 A body is dropped from a height of 2 m It penetrates into the sand on the ground through

1 10 J 3 0 98 J will be 1 2 9 8 J 4 98 J 6 A stone is projected vertically up to reach maximum height h The ratio of its kinetic energy 4h 5 to potential energy at a height will be 1 5 4 2 4 5 3 1 4 4 4 1 A block of mass 16 kg is moving on otionl logo 6

A small glass bead of mass m initially at rest starts from a point at height h above the horizontal and rolls down the inclined plane AB as shown Then it rises along the inclined plane BC Assuming no loss of energy the time period of oscillation of the glass bead is C A C 8h V g sin 0 sin 0 X 8h 1 g sin 0 1 sin 02 0 B B 2 D 14h 1 1 sind 5g sin0 sin 02 8h 1 5g sin 0 4 1 sin 02

7 When a conducting wire XY is moved towards the right a current flows in the anti clockwise direction Direction of magnetic field at point O is X o Y 1 Parallel to motion of wire 2 Along XY 3 Perpendicular outside the paper 4 Perpendicular inside the paper

13 Find the velocity of centre of mass of the system shown in the figure AMU y X o a 2 2 3 3 c 2 2 5 i 3 3 213 2 kg 1 kg 30 2 ms 1 b 4i 2 ms 1 13 d None of these

Juggler keeps on moving four balls in the air continuously such that each ball attains 20 m height When the first ball leaves his hand the position of the other balls in metre height will be A 10 20 10 C 5 51 20 B 15 20 15 D 5 10 20

vector A boat appears to go with 36 km h to a ship sailing at 18 km h northwards If the boat actually travels in east direction it s speed is 1 5 m s 2 5 2 m s 3 5 3 m s 4 10 m s

A juggler is showing a trick with n balls When one of the balls is in his hand all of the rest are in flight If each ball rises to a height of h then how long does the juggler hold a ball before throwing it up 2 2h n 1 g

6 2 7 A ball falls from a height such that it strikes the floor of lift at 10 m s If lift is moving in the upward directic with a velocity 1 m s then velocity with which the ball rebounds after elastic collision will be 1 11 m s 2 12 m s 4 9 m s

8 A person walks along a straight road from his house to a market 2 5kms away with a speed of 5 km hr and instantly turns back and reaches his house with a speed of 7 5 kms hr The average speed of the person during the time interval 0 to 50 minutes is in m sec 2 1 4 3 2 5 3 5 3 1 20 6 4 1 3

Two straight railway tracks are at right angles to each other At 7 pm a train moving at 30 km h crosses the junction Another train following the other track at 40 km h crosses the junction at 12 midnight When 10 12 pm are the two trains closest to each other

straight road due North While car A starts with an initial velocity of 10 m s and an acceleration of 1 m s car B starts from rest with an acceleration of 2 m s Answer the following questions 36 As seen by a passenger in car A 1 Car B moves backward 2 First the car 8 moves backward and then B forward 3 Car B moves forward 4 First the car B moves forward and then backward 37 As seen by a passenger in car B 1 Car A moves backward 2 First the car A moves backward and then forward 3 Car A moves forward First the car A moves forward and then backward 38 The separation between the cars 1 Continuously increases 2 Continuously decreases First increases then decreases and finally increases again 4 First decreases then increases and finally

7 A force of 72 dyne is inclined to the horizontal at an angle of 60 find the acceleration in a mass of 9 g which moves in the effect of this force in a horizontal direction 1 a 5 cms b 4 cms 1 c 2 ms d 3 ms 1

Two particles are moving in the same direction in a straight line with velocities u and u respectively u U Fig 1 37 Before the collision the distance between the two particles will decrease and their velocity of approach will be u u After collision their separation increases with

Is it possible that the train in which you are sitting appears to move while it is at rest Explain You are moving towards your home Is your home at rest with respect to you or is it moving with respect to you Explain Is there any object in this universe which is at rest Support your answer with explanation

Using following data draw time displacement graph for a moving object Time s Displacement 0 2 4 6 8 10 12 14 16 m Use this graph to find average velocity for first da form 6420

A car makes a displacement of 100 m towards east and then 200 m towards north Find the magnitude and direction of the resultant 1 223 7m tan 2 N of E 2 223 7m tan 2 E of N 3 300m tan 2 N of E 4 100m tan 2 N of E

2 A small block slides without friction down an inclined plane starting from rest Let S be the distance travelled from time Sn Sn 1 t n 1 to t n Then a c 2n 1 2n 2n 1 2n 1 is IIT JEE Screening 2004 b d 2n 1 2n 1 2n 2n 1

5 The system shown in the figure can move on a smooth surface The spring is initially compressed by 6 cm and then released Then 2 1 3 kg k 800 N m T 1 time period is sec 5 6 kg 2 amplitude of 3 kg block is 2 cm 3 maximum momentum of6kg block is 2 4 kgm s

25 What will be the tension T and T in the given figure T T 36 N T 6ON6N T 5 kg 4 kg 3 kg 78 N

17 For which of the following position x time graph for the motion of a body the acceleration is negative initially 1 3 2 XA 4 E w w a 1

A particle starts from rest with a uniform acceleration It travels a distance x in first two seconds a distance y in the next two seconds Then A y x B y 2x C y 3x les A dos10 D y 4xw to nup sdT

A ball is projected vertically up with speed 20 m s Take g 10 m s2 1 It covers a distance of 5 m in 2nd second of its motion T 2 The displacement in 2nd and 3rd second are equal 3 The distance covered in 2nd and 3rd second are equal 4 The average speed for first 4 seconds is zero

11 The velocity time and acceleration time graphs of a particle are given as a c Its position time graph may be given as K Time Position Acceleration Position Time b Velocity d Position Position Time Time

A ball is dropped from a long tower One second after its fall air provides horizontal acceleration o 49 m s Total displacement covered by the ba 3 after 4 s of its fall will be take g 10 m s 1 133 3 m 2 100 m 3 227 8 m 4 150 m

A body is thrown with velocity 20 m s at an angle of 60 with the horizontal Find the time gap between the two positions of body where velocity of body makes an angle of 30 with horizontal 1 1 15 s 3 1 s 0 95 s 1 5 s 2 4

2 17 At the moment t 0 the force F kt is applied to a small permanent direction of this force forms an angle 8 with the body of mass m resting on smooth horizontal plane The horizontal Find i The velocity of the body at the moment of its breaking off the plane in The distance traversed by the body up to this moment

ents usly p to 40 An object is moving with a uniform accele ration which is parallel to its instantaneo direction of motion The displacement velocity v graph of this object is 1 3 S K 2 4

A cubical block of mass M and edge length slides down a rough inclined plane of inclination 0 with a uniform velocity The torque of the normal force on the block about the centre of cube has a magnitude HO 1 Zero 1 3 mg sin 0 sin 1 na 2 mgl cos 008 2 4 malcos