Kinematics Questions and Answers

1 57 A particle moves along a horizontal straight line with a velocity time relationship as shown in the figure 1 129 The total distance moved by the particle is A 39m C 26m 8 S M 12 2 Figure 1 129 5 t s I B 13 m D 2 6m

22 A batsman hits back a ball of mass 0 15 kg straight in the direction of the bowler without changing its initial speed of 12 m s If the ball moves linearly then the impulse imparted to the ball is a 18 Ns b 2 8 N c 3 6 Ns d 4 2 Ns 63

1 The angle between A 1 jand B 1 1 is a 45 c 45 b 90 d 180 2 Which one of the following statements is true a A scalar quantity is the one that is conserved in a process b A scalar quantity is the one that can never take negative values c A scalar quantity is the one that does not vary from one point to another in space d A scalar quantity has the same value for observers with different orientations of the axes 3 Figure shows the orientation of two y4 vectors and in the xy plane If a b and v pi qj Which of the following is correct a a and p are positive while b and q are negative b a p and b are positive while q is negative c a q and b are positive while p is negative d a b p and q are all positive 5 The horizontal range of a projectile fired at an angle of 15 is 50 m If it is fired with the same speed at an angle of 45 its range will be a 60 m b 71 m d 141 m c 100 m temperature area Out of these the only vector quantities are 6 Consider the quantities pressure power energy impulse gravitational potential electrical charge a Impulse pressure and area b Impulse and area c Area and gravitational potential d Impulse and pressure 7 In a two dimensional motion instantaneous speed is a positive constant Then which of the following are necessarily true a The average velocity is not zero at any time b Average acceleration must always vanish c Displacements in equal time intervals are equal d Equal path lengths are traversed in equal intervals 8 In a two dimensional motion instantaneous speed v is a positive constant Then which of the following are necessarily true 4 The component of a vector 7 along x axis will have 9 Three vectors A B and C which is false maximum value if a F is along positive y axis b F is along positive x axis c makes an angle of 45 with the x axis d F is along negative y axis a The acceleration of the particle is zero b The acceleration of the particle is bounded c The acceleration of the particle is necessarily in the plane of motion d The particle must be undergoing a uniform circular motion add up to zero Find a AXB xC is not zero unless B C are parallel b A x B C is not zero unless B C are parallel c If A B C define a plane Ax B xC is in that plane d Ax B C A B C C A B 10 It is found that A B A This necessarily implies a B 0 b A B are antiparallel c A B are perpendicular d A B 0

ID d A X 17 At a particular instant of time position vector F velocity vector and angular position of a particle traversing a path AB are shown in the figure Here is the angle made by the velocity vector with the positiv x axis Which of the following statements is are correct a Modulus a Modulus of angular velocity is de usin 0 dt r d 0 b Modulus of tangential component of acceleration is r dt de c Modulus of normal component of acceleration is v dt d Ja Modu d Modulus of normal component of acceleration is u dt

Ex 1 Aperfectly elastic ball is thrown from the foot of a plane inclined atan angle to the horizon If after striking the plane at a distance from the point of projection it rebounds and retraces its former path show that the velocity of projection is

If a particle travels distance S S and s3 taking equal time to cover the respective distances Find average speed of the particle if it travels with a velocity V V and v3 for the respective distances 1 3 V V V3 2 S S S3 V V3 V2 S S S3 S V 3 2 V V V3 2 3 4 both 2 and 3

1 34 A parachutist drops freely from an aeroplane for 10 s before the parachute opens out Then the descends with a net retardation of 2 5 m s If he bails out the plane at a height of 2495 m and g 10 m s his velocity on reaching the ground will be A 2 5 m s C 5 m s B 7 5 m s D 10 m s

1 28 The following shows the time velocity graph for a moving object The maximum acceleration will be V m sec 60 40 20 0 A 1 m sec C 3 m sec 10 A 1 m sec C 3 m sec A 20 1 1 B 30 40 50 Figure 1 120 60 B 2 m sec D 4 m sec 1 29 In the above question the magnitude of retardation will be 70 t in sec B 2 m sec D 4 m sec 1 33 the p veloc A C 1 34 befo reta 249 be A C 1 3 WI pa

c a q and b are positive while p is negative d a b p and q are all positive The component of a vector 7 along x axis will have maximum value if a F is along positive y axis b F is along positive x axis c 7 makes an angle of 45 with the x axis d F is along negative y axis The horizontal range of a proiectile fired at an angle 9 B Th wh a b c d

1 43 The figure 1 125 shows the acceleration versus time graph of a train If it starts from rest the distance it travels before it comes to rest is 1 1 sugit A 30m C 13m lug a m s 2 O it 1 5 2 3 4 t s Figure 1 125 B 26m D 40m

99 A fighter plane flying horizontally at an altitude of 1 5 km with speed 720 km h passes directly overhead an anti aircraft gun At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s to hit the plane Take g 10 ms a sin c cos b sin d cos

C 1 30 A rocket is fired vertically upwards and moves with net acceleration of 10 m s After 1 min the fuel is exhausted The time taken by it to reach the highest point after the fuel is exhausted will be A 10 sec C 30 sec B 20 sec D 60 sec 1 36 strai dista

A rocket is fired vertically up from the ground with an acceleration 10 metre per second square if its fuel is finished after 1 minute then calculate A Maximum velocity attained by a rocket in ascending motion B Height attained by rocket before fuel is finished C Time taken by rocket in the whole motion D Maximum height attained by rocket

What is the maximum height attained by an object that is projected from the surface of the earth with a velocity that is one third of the escape velocity Radius of the Earth R 1 R 4 2 R 2 3 R 8 4 R 5

5 Two towns A and B are connected by regular bus service with a bus leaving either direction every T minutes A th cycling with a speed of 20 km h in direction from A to B notices that a bus goe past him every 18 min in the direction of his motion and every 6 min in the opposite direction The speed with which assume constant buses ply on road is 1 40 km h 2 60 km h 3 75 km h 4 80 km h NCERT Pg 56

5 Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes A man cycling with a speed of 20 km h in the direction from A to B notices that a bus goes past him every 18 min in the direction of his motion and every 6 min in the opposite direction The speed with which assumed constant buses ply on road is 1 40 km h 2 60 km h 3 75 km h NCERT Pg 56

An archer standing on a 15 degree slope shoots an arrow at an angle of 27 degrees above the horizontal How far below its original point of release does the arrow hit if it is shot with a speed of 36 m s from a height of 1 92 m above the ground Your answer

A ball is thrown straight upward with a speed v from a point h meter above the ground The time taken for the ball to strike the ground is A 1 1 g 6 D C 1 OD 2hg 2 v 2hg v 2 B D 1 2 2hg g 2hg 2 v

circular motion is towards the centre only if the speed is constant 80 A particle is moving on a circular path of radius r with uniform speed v What is the displacement of the particle after it has described an angle of 60 a 2 c r b r 3 d 2r

During the first 18 min of a 60 min trip a car has an average speed of 11 ms What should be the average speed for remaining 42 min so that car is having an average speed of 21 ms for the entire trip A 25 3 ms C 31 ms B 29 2 ms D 35 6 ms

A body is moving on a straight line with initial velocity 12 m s and initial retardation 4 m s It s retardation decreases to zero linearly in time t What is the value of time t in sec if the body will completely stop moving at this time

produce the same number of beats with a standard tuning fork of 456Hz The possible frequency of the note B is A 228Hz B 456 Hz C 456 5 Hz D 458 5 Hz SECTIO N II NUMERICAL VALUE TYPE This section contains 8 questions Each question is numerical value For each question enter the correct numerical value in decimal notation truncated rounded off to second decimal place e g 6 25 7 00 0 33 30 30 27 127 30 Marking scheme 3 for correct answer 0 if not attempted and 0 in all other cases 7 A particle is projected with a velocity 2 Jag so that it just clears two walls of equal height a which are at a distance 2 a apart Find the time of passing in seconds between the walls given a 40m and g 10m s

4 Two trains P and Q of length 300 m and 500 m are moving on two parallel tracks each with a uniform speed of 72 km h in the same direction with Q ahead of P The driver of train P decide to overtake train Q and accelerates by 2 0 m s2 if after 40 s the guard of P just brushes past the driver of Q then the original distance between the trains NCERT Pg 56 is 1 450 m 2 650 m 4 1300 m

The linear mass density of a ladder of length increases uniformly from one end A to the oth end B i Form an expression for linear mass density as a function of distance x from end A whe linear mass density 2o The density at one end being twice that of the other end ii Find the position of the centre of mass from end A

9 A boy standing on a lift moving with speed 10 m s The lift is open from top The boy throws the ball with maximum speed of 24 5 m s in upward direction In how much time the ball returns to the hand of boy g 9 8 m s 1 10 s 3 7 5 s 2 5 s 4 6 s

d not a constant vector 5 What is approximately the centripetal acceleration in units of acceleration due to gravity on earth g 10 m s of an air craft flying at a speed of 400 m s through a circular arc of radius 0 6 km a 26 7 b 16 9 c 13 5 d 30 2

19 When alpha particles are directed onto atoms in a thin metal foil some make very close collisions with the nuclei of the atoms and are scattered at large angles If an alpha particle with an initial kinetic energy of 5 MeV happens to be scattered through an angle of 180 which of the following must have been its distance of closest approach to the scattering nucleus Assume that the metal foil is made of silver with Z 50 O 1 22 50 1 3 fm 2 9 10 14 m O O 3 0 10 8 m O 1 0 10 12 m 1 7 10 7 m

a 52 A cricket ball is thrown at a speed of 30 m s in a direction 30 above the horizontal The time taken by the ball to return to the same level is Take g 10 m s a 2 s b 3 s d 5 s the distance from the c 4 s

c 23 5m 55 A cricketer can throw a ball to a maximum horizontal distance of 100 m With the same speed how much high above the ground can the cricketer throw the same ball a 50 m b 100 m c 150 m d 200 m

vii A mass of 6 x 1024 kg equal to the mass of the earth is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 108 m s What should be the X radius of the sphere 8 893 mm

12 A particle starts from rest and moves along a straight line with constant acceleration The variation of velocity with displacement S is 13 A particle starts from rest at time t 0 and moves on a straight line with acceleration as shown in the fig the speed of the particle will be maximum after time a Is b 2s c 3s d 4s a in ms 10 O 10 DI 2 51 4 4 in second

4 12 hours 5 19 A particle is projected vertically up with gRE from earth surface The velocity of particle at height equal to the 4 maximum height reached by it is velocity v 1 GRE 4 laRr 2 NCERT Pg 196 GRE V 3

6 An aeroplane flying horizontally with a speed of 360 km h releases a bomb at a height of 490 m from the ground If g 9 8 m s it will strike the ground at a 10 km c 1 km b 100 km d 16 km

A self propelled vehicle of mass m whose engine delivers a constant power P has been P mv travelled by it assuming no friction to increase the velocity of the vehicle from V to V acceleration a What is the distance

79 Which of the following statements is incorrect a In one dimension motion the velocity and the acceleration of an object are always along the same line b In two or three dimensions the angle between velocity and acceleration vectors may have any value between 0 and 180 c The kinematic equations for uniform acceleration can be applied in case of a uniform circular motion

24 Two blocks 4 kg and 2 kg are sliding down on a fixed inclined plane as shown The acceleration of 2 kg block is 0 2 0 3 4 kg 2 kg 30 2 2 69 ms 2 4 4 13 ms 1 1 66 ms 2 3 3 212 ms 25 The coefficient of friction between the tyres and the horizontal road is 0 25 The maximum speed at which a car can be driven round a curve of radius 40 m without skidding is g 10 m s 1 15 ms 1 3 12 ms 1 2 20 ms 1 4 10 ms 1 dical

to ne 6 40 A body falls freely towards the earth from a height 2R above the surface of the earth where initially it was at rest If R is the radius of the earth then its velocity on reaching the surface of the earth is A 4 3 gR 4 C gR B 2 gR D 2gR

v2 m PROJECTILE MOTION Which of the following is true regarding projectile motion a Horizontal velocity of projectile is constant b Vertical velocity of projectile is constant c Acceleration is not constant d Momentum is constant

A person driving a car with a speed of 72 km h observes a boy crossing the road at a distance of 100 m from the car Driver applies the brakes and retards the car with a retardation of 5 m s and is just able to avoid this accident The reaction time of driver is NCERT Pg 51 1 2 0 s 2 2 4 s 3 3 0 s 4 2 8 s ka Four

D A projectile is projected with initial velocity 10 20 m s from the ground The velocity of the body just before hitting the ground is 1 10 20j 2 10 20j 3 10 20 4 10 20

1 1 FOL 2 15 16 3 m s 4 1 5 in metres 6 Above diagram represents a multiflash photograph of an object P moving along a horizontal surface The successive positions as indicated in the diagram are separated by equal time intervals of 1 second The first flash occurred just as the object started to move and the last just as it came to rest The average speed of the object during the motion is 2 7 8 16 15 9 m s 10

m above y with a stone to 15 s ch which 60 Two projectiles are fired from the same point with the same speed at angles of projection 60 and 30 respectively Which one of the following is true a Their range will be the same b Their maximum height will be the same c Their velocity at the highest point will be the same d Their time of flight will be the same ites that for angles of projection of a

56 The ceiling of a hall is 40 m high For maximum horizontal distance the angle at which the ball may be thrown with a speed of 56 m s without hitting the ceiling of the hall is b 30 a 25 c 45 d 60 57 In the question number 56 the maximum horizontal distance covered by the ball will be

A hose pipe on ground shoots a stream of water upwards at an angle of 60 to horizontal with a velocity of 10 ms 1 The height at which the water will strike a wall 5 m away is 1 2 46 m 2 3 76 m 3 4 9 m 4 8 66 m A projectile is projected with an initial velocity of v 61 81 ms The magnitude of change in velocity 1 5 s after firing will be g 10 ms 1 8 ms 1 2 16 ms 1 3 1 ms 1 4 15 ms 1

64 51 The relation between the time of flight of projectile T and the time to reach the maximum height is a T 21 c Ty d T 2 tm

Point A moves uniformly with velocity v so that the vector v is continually aimed point B which in its turn moves rectilinearly and uniformly with velocity u v At th initial moment of time v is perpendicular to u and the points are separated by a distance d How soon will the points converge

54 Two balls are projected at an angle 8 and 90 9 to the horizontal with the same speed The ratio of their maximum vertical heights is a 1 1 b tane 1 d tan 0 1 c 1 tane 55 Two particles are proiected in air with speed u

Four particles are projected with same initial speed at angles of 30 42 47 and 60 with vertical The horizontal range of the projectile is largest for one projected at an angle of 1 60 2 30 3 42 4 47

4 A motorboat is racing towards north at a speed of 10 m s wind start to blow with a speed of 10 m s at 60 east of north The resultant velocity of boat is 1 10 3 m s at 30 east of north 2 10 3 m s at 30 north of east 3 20 m s at 30 west of north

c Ty d T 2 tm 52 A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with a speed of 15 m s The time taken by the stone to reach the ground is a 5 s b 10 s c 12 s d 15 s 60 g Two p the sa respec a II b T c T