Kinematics Questions and Answers

P The brake mechanism used to reduce the gun recoil consists of a piston attached to a barrel moving in a fixed cylinder filled with oil As the barrel recoils with an initial velocity vo the piston moves and oil is forced through the orifices in the piston causing the piston and cylinder to decelerate according to a kv where k Determine its velocity as a function of time velocity as a function of displacement and displacement as a function of time Also roughly sketch v t vs time v x vs displacement and x t vs time 10 ol Piston a kv

A car starts from rest and again comes to rest after travelling a distance of 12k m in 1 8 hour It s maximum velocity in between is 12km h In its journey accel eration and retardation are both unifor m and the value of acceleration is half that of retardation How long does the car travel with uniform velocity

radius r and mass m each are in equilibrium as shown in the figure What is the maximum mass of cylinder C that can be put on top of cylinder A and B such that the system remains in equilibrium Given that radius of cylinder C is 2r 7 Assume that axi of all four cylinder are parallel to each other A 2m 5 B 4m 5 48 Smooth fixed Cylindry C 6m 5 D 8m 5

ALLEN HAVE CONTROL 1 HAVE CON BEWARE OF NEGATIVE MAR 3 7 m s HAVE PATIENCE A particle is moving on x axis with speed v x 9 where x is the distance travelled by the particle Acceleration of the particle is 1 4 5 m s2 2 3 m s2 w m s 1 35 SEL 4 1 4 3

A man is running up hill with a velocity 21 31 m s w r t ground He feels that the rain drops are falling vertically h with velocity 4 m s If he runs down hill with same speed find v m A body is projected with velocity u from point A as shown in figure

A boy can swim in still water at 1 m s He swims across a river flowing at 0 6 m s which is 336 r wide If he travels in shortest possible time then the resultant velocity of swimmer must be A perpendicular to river flow B in a direction making obtuse angle with river flow C in a direction making acute angle with river flow D cant be determined

The brake mechanism used to reduce the gun recoil consists of a piston attached to a barrel moving in a fixed cylinder filled with oil As the barrel recoils with an initial velocity vo the piston moves and oil is forced through the orifices in the piston causing the piston and cylinder to decelerate according to a kv where k Determine its velocity as a function of time velocity as a function of displacement and displacement as a function of time Also roughly sketch v t vs time v x vs displacement and x t vs time 10 Piston ol a kv

Q 27 The minimum speed in m s with which a projectile must be thrown from origin at ground so that it is able to pass through a point P 30 m 40 m is g 10 m s

A car travelling at a speed of 30km h is brought to a halt in 4m by applying brakes If the same car is travelling at 60km h it can be brought to halt with the same braking power in b 16m a 8m c 24 m d 32m

d Maximum height attained by rocket A particle is dropped from the top of a tower During its motion it covers part of height of the last 1 second Then find the height of tower 9 25

3 Change the K E of a charged particle 4 Stop a moving charged particle 3 A stone is released from an elevator going up with an acceleration a The acceleration of stone afte the release is 1 a upward 2 ga upward 3 g a downward 4 g downward

A mountain climber is sliding down a vertical rope Her total mass including the equipments is 65 kg By adjusting the friction on the rope she controls the tension force on the rope as a function of time is shown in the figure The speed of the mountaineer at the end of 2 sec if she starts from rest is Take g 9 8 m s A 2 25 m s B 4 5 m s C 5 m s ic joined to the end of a slope 4T N m 637 312 D 2 5 m s 0 2

Consider a pendulum consisting of a massless string with a mass on the end The mass is held with the string horizontal and then released The mass swings down and then on its way back up the string is cut at point P when it makes an angle of 0 with the vertical What should be so that the mass travels the largest horizontal distance from P by the time it returns to the height it had when the string was cut A tan 3 B tan 3 C tan D tan 1 cut P

A body traveling along a straight line with a uniform acceleration has velocities 5 m s at a point A ar 15 m s at a point B respectively If M is the midpoint of AB then A The ratio of times taken by the body to cover distances MB and AM is B The velocity at M is 5 5 m s 5 5 1 m s 2 D The product of the acceleration and the distance AB is 100 m s C Average velocity over AM is 5 1 2

A particle is moving in a circular orbit with a constant tangential acceleration After a certain time t has elapsed after the beginning of motion from rest the angle between the total acceleration and the direction along the radius becomes equal to 45 What is the angular acceleration of the particle at this instant

11 A ring of mass m slide from rest on the smooth rod as shown in the figure due to the block of mass m Pully and string are massless Then find the speed of ring when the string become straight Given 0 60 A 4 gh C 2 2gh B 2gh D 8 gh ENTHUSIAST

relative velocity of A w r t B Two bodies A and B are 10 km apart such that B is to the south of A A and B start moving with the same spee 20 km hr eastward and northward respectively then find N a relative velocity of A w r t B b minimum separation attained during motion time elapsed from starting to attain minimum separation c W S E

pr 2 Two planes fly at the same height with speeds v 800 km h and v 600 km h respectively The planes ap ct proach each other at a certain moment of time the plane tra es jectories are perpendicular to each other and both planes are at ch the distance a 20 km from the intersection points of their tra ay a jectories Find the minimal distance between the planes during and their flight assuming their velocities will remain constant a 20 km his lat cult se of cult cepts e for etric tivos V 800 km h a 20 km A 600 km h

c 1 x 42 The displacement x of a particle varies with time t as at be t where a b a and are positive x ae constants The velocity of the particle will go on decreasing with time b be independent of a and B c drop to zero when a d go on increasing with time Va dr Je

The position of a particle along X axis at time t is distance travelled in the interval t 0 to t 1 are given by x 2 t 3t The displacement and the respectively a 22 b 2 2 5 c 0 2 d 2 21 lled to fall freely from rest The ratic

2 42 4 The magnitude of final acceleration is 6 m s Select the correct formulae for uniformly accelerated motion along a straight line 1 V U v u at s U V 2 3 s 3 s vt s vt 21at 4 s v u 2a Use this

Balloons with constant ascending velocity can be used investigate wind velocities at various heights The given graph of elevation angle against time was obtained by observing a such balloon The balloon was released at distance L 1 km from the point of observation and it seemed to be rising dir ectly upwards Knowing that wind velocity near the ground was zero find the balloon s height at time t 7 min after its start and wind velocity at this height Aa deg 60 40

ear teacher pls Solve option 2nd 3rd and 4th 16 A ball P is projected vertically upwards with initial speed 40 ms Another ball Q is projected vertically upward along the same line 2 s later with speed v Neglect air friction and take g 10 ms Choose the correct option s among the following 1 If v 50 ms 1 the ball Q will meet ball P when P is instantaneously at rest 2 If 30 m s v 50 m s the ball Q will meet ball P when P is still ascending 3 If 30 m s v 50 m s the ball Q will meet ball P when P is descending 4 If v 50 m s then Q will meet P when P is still ascending

c 32 ms 41 A point moves in a straight line so that its displacement acceleration is a 1 x c 1 x 2 x at time t is given by x t 1 Its b 1 x 3 d 1 x oment x of a particle varies with tim ositi

A 75 kg skier starts from rest at a height of 20 m above the end of ski jump ramp As the skier leaves the ramp his velocity makes an angle of 30 with the horizontal Neglect the effects of air resistance and assume the ramp is frictionless The maximum height h of his jump above the end of the ramp is 20m 1 5m 3 15 m 2 10m 4 20 m

35 A particle moves a distance x in time t according to x t 5 The acceleration of particle is equation proportional to velocity 3 2 c distance 2 un b distance 2 d velocity 2 3 vertically upward with a speed

38 The binding energy of an electron in the ground state of He is equal to 24 6 eV The energy required to remove both the electrons is 20 a 24 6 eV c 79 eV A photon is emitted b 49 2 eV d 38 2 eV

1 Q Advanced Level The displacement x of a particle moving along axis varies with time asx 2F 38 m where t is in seconds then 1 The particle retums to its initial position after The particle comes to rest at t Initial velocity of particle is zero Maximum velocity in positive x direction is m s A particle moves in a straight line under an acceleration varying linearly with time Its velocity time graph is shown in figure Then v m s 37 45 1 The particle comes to rest at t 7s 2 The initial velocity of particle is 1 m s 3 Maximum velocity of particle is 2 m s 4 The acceleration of particle is zero at t 3 s A particle starts from rest at x and acceleration varies with X as shown in the figure Then a m s que 2010 r x m 1 The particle comes to rest at x 20 m Maximum velocity in positive x direction is 4 6 m s Velocity at x 10 m is 60 m s Distance covered by particle till it returns to initial position is 80 m Py wo stones are thrown vertically upwards simultaneously from the same point on the ground with velocities y 40 m s and topg Motion in a Straight Line 119 relative separation between stones v v relative velocity of two stones a a relative acceleration of two stones 1 2 0 a V V os G y y O agan The acceleration a of a particle moving in a straight line varies with velocity v as a 1 v m s where v is in m s If initially the particle was at rest then poy Per Maximum velocity of the particle will be 1 m s 2 Maximum acceleration is 1 m s 3 The particle will finally come to rest Velocity of particle at t n2 s is 13A ball is projected vertically upwards from ground with velocity v 24 m s Assume the acreside produces a constant retardation of 2 mis meh g 10m s 1 The maximum height attained is 288 m 2 Time of ascent is more than time mvs

9 The displacement x of a particle varies with time t as x ae at be t where a b a and are positive constants The velocity of the particle will 2005 a Be independent of B b Drop to zero when a c Go on decreasing with time d Go on increasing with time

Find its velocity after 3 seconds in m s 9 ms s Fin The drops of water fall from the 9 m high roof of a building at regular interval of time The first drop reaching the ground at the same instant when fourth drop starts falling Find the distance between second and third drops in m 6 The position of a particle is given by x t 212

A diver springs upward from a board that is 3 30 m above the water At the instant she contacts the water her speed is 11 8 m s and her body makes an angle of 74 5 with respect to the horizontal surface of the water Determine her initial velocity both a magnitude and b direction

A particle of mass m is moving along the x axis with speed v when it collides with a particle of mass 2 M initially at rest After the collision the first particle has come to rest and the second particle has split into two equal mass pieces that are shown in the figure Which of the following statements correctly describes the speeds of the pieces 0 0 m 2m Before collision A B C x axis m m After collision Each piece moves with speed v Each piece moves with speed v 2 x axis One of the pieces moves with speed v 2 the other with speed greater than v 2 Jy 1 6 Correct 0 2 7 MY PERFORMA SCORE 1 00 W out of 32

3 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 he is a h 2h 3h3 h h3 3 5 c h 3h and h3 3h b h

3 Aman walks 30 m towards north then 20 m towards east and the last 30 2 m towards south east The displacement from origin is 1 10 m towards west A 2 50 m towards east 3 60 2 m towards north west 4 60 2m towards east north 3 with 4 with 19 A man east T v due 1 2v 20 A car tra

A and stone is dropped into 45 seconds later is The Second stone initial velocity of Vo 4 seconds later H 336 mls Seund stone a the determine the thrown and well Sound of with no intial velocity um pact is unto the splash is Vetouit the well with an heard heard after velocity of the dound wis initial velocity of the

44 Figure shows the force displacement graph Work done by an object to cover first 30 m distance will be A 200 J C 100 J B 400 J D 300 J Force N 501 40 30 20 10 10 20 30 Displacement m 50

3 Two boys are standing at the ends A and B of a ground where AB a The boy at B starts running in a direction perpendicular to AB with velocity v The boy at A starts running simultaneously with velocity v and catches the other boy in a time t where t is 2005 a a v c a v v b a v v d a v v orticle varies with time t

A jet of water discharged from a nozzle hits a screen 6 m away at a height of 4 m above the centre of a nozzle When the screen is moved 4 m further away the jet hits it again at the same point Assuming the curve described by the jet to be parabolic find the angle at which the jet is projected

A body of mass 2 kg has an initial velocity of 3 meters second along OE and it is subjected to a force of 4 N in 2 direction perpendicular to OE The distance of the bods from O after 4 seconds will be d 48 m

An object is moving in a straight line with constant acceleration It covers 65 m distance in 5th second and 105 m distance in 9th second The distance covered by it in 20 seconds is 1000 m 800 m 1800 m 2400 m

I P L In a match of R C B K player Chris Gayle hits a six and the ball falls on the roof of the stadium 60m away from him If the time of flight of the ball is 4 sec and the ball strikes the roof of the stadium at an angle of 45 from the horizontal in the downward direction then C G X 60m 45 When Gayle hit the ball then the ball The initial move was

A car A is going north east at 80 km hr and another car B is going south east at 60 km hr Then the direction of the velocity of A relative to B makes with the north an angle a such that tana is A 1 7 C 4 3 B 3 4 D 3 5

A 1500 kg satellite orbits the Earth at an altitude of 2 5x10 6 m What is its 6 points a orbital speed b period c kinetic energy Oa 7590 m s b 5274 s c 4 32 x 10 10 J Oa 8590 m s b 6774 s c 3 52 x 10 10 J Oa 7590 km s b 5274 s c 4 32 x 10 12 J O a 8590 km s b 6774 s c 3 52 10 10 kJ

A point traversed half the distance with a velocity vo The remaining part of the distance was covered with velocity v for half the time and with velocity v for the other half of the time Find the mean velocity of the point averaged over the whole time of motion

5 The minimum force required to move a body up an inclined plane is two times the minimum force required to prevent it from sliding down the plane If co efficinet of friction between the body and and inclined plane is the angle of inclined plane is

The answer given for this question was 3 10 m s But I d on t understand the explanation given in the Aakash itutor solution book was delta v 5 5 10 But a v u t then ho w v u can work in the question 2 A ball strikes the floor vertically downward with a speed 5 m s and rebounds with the same speed The magnitude of its change in velocity will be 1 Zero 2 5 m s 3 10 m s 4 40 m s

3 10 Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2 0 atm and temperature 17 C Take the radius of a nitrogen molecule to be roughly 1 0 A Compare the collision time with the time the molecule moves freely between two successive collisions Molecular mass of N 2 28 0 u

If f is zero then p is constant or zero simultaneously v can be zero or constant And kinetic energy depends on final and initial velocity b ut velocity is constant here so it shouldn t vary but ans wer is given that option 2 and 4 are correct JM 10 If the net force acting on the system of particles is zero then which of the following may vary 1 Momentum of the system 2 Kinetic energy of the system 3 Velocity of centre of mass 4 Position of centre of mass 11 A mortar fires a shell of mass M which explodes into tun ninnan af mann 1115 and AM 5 at the

A proton is fired to the right into a region with a uniform electric field with magnitude of 5 8x105N C pointing to the left The proton travels 5cm before coming to rest part A What was the proton s initial speed part B How long did it take the proton to come to rest

Three identical smooth spheres each of mass 3 3 2 kg on a smooth horizontal plane are in contact with one another and are kept together by an endless string in the plane of their centers just fitting them when a fourth identical sphere is placed on them the k tension in the string is newton then find the value 2 of k Take g 10m s THREAD