KINEMATICS - dkxubxs5kklfj.cloudfront.net

CONTENTS

KEY CONCEPT - 2 - 3

EXERCISE-I - 4 - 10

EXERCISE-II - 11 - 14

EXERCISE-III - 15 - 17

ANSWER KEY - 18

PHYSICS

GOOGOL-XIII

KINEMATICS

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PHYSICS NEEL KAMAL SETHIA (NKS SIR)

KINEMATICS

Change in position vector is called displacement.

displacement involves only the original and final position.

Length of path traversed by a body is called distance. It is a scalar quantity, as length of path has no

indication of direction in it.

Average Velocity and Instantaneous Velocity :

Vavg = t

s

= 12

12

tt

rr

Instantaneous velocity is the value that t

rrv 12

avg

approaches in the limit as we shrink the time interval

t so we are able to find instantaneous velocity about that instant

dt

rdv

Average Speed and Instantaneous Speed :

Average speed = total distance travelled

total time

Instantaneous speed = Speed at a perticular instant or magnitude of instantaneous velocity.

Acceleration :

Definition: Rate of change of velocity is called acceleration and is directed along the change in velocity.

The average acceleration aavg over a time interval t is

aavg = 12

12

tt

vv

=

t

v

where the particle has velocity v1 at time t1 and then velocity v2 at time t2.

The instantaneous acceleration (or simply acceleration) is the derivative of the velocity with respect to

time.

a = dt

vd

PROJECTILE MOTION (2D MOTION) :

LEVEL GROUND PROJECTION

Time of flight(T)

T = g

sinu2

Maximum Height(H) Ux = ucos , uy = usin

H = g2

sinu 22

Horizontal Range(R)

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R = g2

2sinu2 =

g

uu2 yx

PROJECTION ON INCLINED PLANE

x-axis y-axis

ux = u cos (–) uy = u sin (– )

ax = – g sin ay = – g cos

vel. at any time t = vel. at any time t =

vx = u cos (–) – g sin t vy = u sin ( – ) – g cos t

Time of flight

T =

cosg

)(sinu2

Maximum height (Relative to inclined plane)

H =

cosg2

)(sinu 22

Range along the inclined plane

R =

2

2

cosg

]sin)2([sinu

RELATIVE MOTION

REFERANCE FRAME :

Reference frame is an axis system from which motion is observed.

B

BAr

xA

O x

y

Br

y

Ar

From our knowledge of vectors we can deduce that Br

= Ar

+ BAr

thus BAr

= Br

– Ar

Position of B from refrence frame of A is BAr

.

Differentiating this equation wirth respect to time we get BAv

= Bv

– Av

(Velocity of B w.r.t. A)

On further differentiating we get

BAa

= Ba

– Aa

(Acceleration of B w.r.t. A)

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EXERCISE-I

1. A car, moving with a speed of 50 km h–1, can be stopped by brakes in minimum 6m distance. If the same car

is moving at a speed of 100 km h-1, the minimum stopping distance is

(A) 24 m (B) 6 m (C) 12 m (D) 18 m

2. A car moves with a speed of 60 km/hr from point A to point B and then with the speed of 40 km/hr from point

B to point C. Further it moves to a point D with a speed equal to its average speed between A and C. Points

A, B, C and D are collinear and equidistant. The average speed of the car between A and D is :

(A) 30 km/hr (B) 50 km/hr (C) 48 km/hr (D) 60 km/hr

3. Acceleration versus velocity graph of a particle moving in a straight line

starting from rest is as shown in figure. The corresponding velocity-time

graph would be

(A) (B) (C) (D)

4. A particle is thrown upwards from ground. It experiences a constant resistance force which can produce

retardation 2 m/s2. The ratio of time of ascent to the time of descent is [g = 10 m/s2]

(A) 1 : 1 (B) 2

3(C)

2

3(D)

3

2

5. AB is the vertical diameter of a circle in a vertical plane. Another diameter CD makes an angle of 600 with

AB; then the ratio of the time taken by a particle to slide along AB to the time taken by it to slide along CD,

is

(A) 1: 1 (B) 2 :1 (C) 31/4 : 21/2 (D) 1: 2

6. Let A, B, C, D be the points on the vertical line such that AB = BC = CD. If a body is released from rest from

position A, the time of fall to travel AB, BC and CD during free fall are in the ratio

(A) 1: 3 2 : 3 2 (B) 1: 2 1: 3 – 2

(C) 1: 2 1: 3 (D) 1: 2 : 3 1

7. Velocity and acceleration of a particle at some instant of time are mˆ ˆ ˆv (2i j 2k)s

and ˆ ˆ ˆa (i 6 j k)

.

Then, the speed of the particle is ..................... at a rate of ..................... m/s2.

(A) increasing, 2 (B) decreasing, 2 (C) increasing, 4 (D) decreasing, 4

8. A particle is projected vertically upward with initial velocity 25 m/s. For its motion during third second, which

of the following statement is correct?

(A) Displacement of the particle is 30 m (B) Distance covered by the particle is 30 m.

(C) Distance covered by the particle is 2.5 m (D) None of these

9. A body is projected at an angle 60° with the horizontal ground with kinetic energy k. When the velocity

makes an angle 30° with the horizontal, the kinetic energy of the body will be

(A) k/2 (B) k/3 (C) 2k/3 (D) 3k/2

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10. A body is projected at time ( t = 0) from a certain point on a planet’s surface with a certain velocity at a

certain angle with the planet’s surface ( assumed horizontal). The horizontal and vertical displacements x &

y (in meter) respectively vary with time t in second as, x = 10 3 t and y = 10 t – t2. Then the maximum

height attained by the body is :

(A) 200 m (B) 100 m (C) 50 m (D) 25 m

11. An object is thrown horizontally from a tower H meter high with a velocity of 2gH m/s. Its speed on

striking the ground will be :

(A) 2gH (B) 6gH (C) 2 gH (D) 2 2gH

12. If R is the range of a projectile on a horizontal plane and h its maximum height, then maximum horizontal

range with the same speed of projection is

(A) 2h (B) 2R

8h(C) 2R +

2h

8R(D) 2h +

2R

8h

13. A particle is projected with velocity 20 m/s, so that it just clears two walls of equal height 10 m, which are

at a distance 20 m from each other. The time of passing between the walls is

(A) 2 s (B) 2 10 s (C) 10 2 s (D) 1 / 2 s

14. A projectile is thrown from ground. With what minimum velocity, the projectile should be thrown so that is

passes through a point (3, 4). (Take g = 10 m/s2)

(A) 3 5 m/s (B) 7.5 m/s (C) 10 m/s (D) 3 10 m/s

15. Two particles are fired from the same point, with speeds 100 m/s and 100 m/s, and firing angles with

horizontal = 60° and 120° respectively. The time after which their velocity vectors become perpendicular to

each other, is

(A) 5 s (B) 5( 3 – 1) s (C) 5 3 s (D) 5 3 / 2 s

16. Two particle A and B are projected simultaneously from a fixed point on the ground. Particle A is projected

on a smooth horizontal surface with speed v, while particle B is projected in air with speed 2v

3. If particle

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

17. A particle is projected with a certain velocity at an angle above the horizontal from the foot of a given plane

inclined at an angle of 45° to the horizontal. If the particle strike the plane normally then equals

(A) tan1(1/3) (B) tan1 (1/2) (C) tan1(1/2) (D) tan1 3

18. A projectle is fired horizontally from an inclined plane (of inclination 30° with horizontal) with speed = 50 m/

s. If g = 10 m/s2, the range measured along the incline is

(A) 500 m (B) 1000/3 m (C) 200 2 m (D) 100 3 m

19. 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

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Paragraph for question nos. 20 to 22

Ram in his Santro accelerates at the rate of ˆ ˆ3 i 2 j m/s2, while Shyam in his Maruti accelerates at

ˆ ˆ6 i 2 j m/s2. They both start from rest at the origin of an xy coordinate system. After 5s.

20. What is Ram's speed with respect to Shyam

(A) 15 m/s (B) 20 m/s (C) 25 m/s (D) 10 m/s

21. How far apart are they

(A) 37.5 m (B) 50.0 m (C) 62.5 m (D) 25.0 m

22. What is Ram's acceleration relative to Shyam?

(A) 5 m/s2 (B) 4 m/s2 (C) 3 m/s2 (D) 1 m/s2

23. A lift is moving in upward direction with speed 20 m/s and having acceleration 5 m/s2 in downward direction.

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/s2

(D) none of these

24. A man travelling in car with a maximum constant speed of 20 m/s watches the friend start off at a distance

100 m ahead on a motor cycle with constant acceleration ‘a’. The maximum value of ‘a’ for which the man

in the car can reach his friend is :

av

100 m

(A) 2 m/s2 (B) 1 m/s2 (C) 4 m/s2 (D) None of these

25. Two particles 1 and 2 are moving with velocities 1

ˆ ˆv 4i 3 j

m/s and 2

ˆ ˆv bi j

m/s respectively. The

position vectors of the particles at time t = 0 are 1

ˆ ˆr 5i 2 j

m and 2

ˆ ˆr 4i 4 j

m. If they collide at t = 3s,

the value of b is

(A) 10

3(B) 5 (C) –1 (D) 7


Ram and Shyam are walking on two perpendicular tracks with speed 3 ms–1 and 4 ms–1 respectively. At a

certain moment (say t = 0 sec) Ram and Shyam are at 20 m and 40 m away from the intersection of tracks

respectively and moving towards the intersection of the tracks.

26. During the motion the magnitude of velocity of ram with respect to shyam, is -

(A) 1 ms–1 (B) 4 ms–1 (C) 5 ms–1 (D) 7 ms–1

27. Shortest distance between them subsequently, is -

(A) 18 m (B) 15 m (C) 25 m (D) 8m

28. The time t when they are at shortest distance from each other subsequently, is -

(A) 8.8 sec (B) 12 sec (C) 15 sec (D) 44 sec

29. A ferry boat is sailing at 12 km/h 30°W of N with respect to a river that is flowing at 6.0 km/h E. As observed

from the shore, the ferry boat is sailing :

(A) 30°E of N (B) due N (C) 30°W of N (D) 45° E of N

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30. A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with

a speed of 5 km/hr, at an angle w.r.t. the river. If AB = BC = 400 m. Then the value of is :

(A) 37º (B) 30º (C) 53º (D) 45º

31. Two boats A & B are moving along perpendicular paths in a still lake at night. Boat A moves with a speed of

3 m/s and boat B moves with with a speed of 4 m/s in the directions such that they collide after sometime.

At t = 0 , the boats are 300 m apart. The ratio of distance travelled by boat A to the distance travelled by boat

B at the instant of collision is

(A) 1 (B) 1/2 (C) 3/4 (D)4/3

32. A boat is moving towards east with velocity 4 m/s with respect to still water and river is flowing towards north

with velocity 2 m/s and the wind is blowing towards north with velocity 6 m/s. The direction of the flag blown

over by the wind hoisted on the boat is:

(A) north-west (B) south-east

(C) tan–1(1/2) with east (D) north

33. Figure shows two swimmers starting from point A and B on opposite banks. They started at same instant

with a constant velocity. Both of them are swimming in a direction parallel to line AB always. The river flows

towards east.

d

B

A

River flow

(A) Swimmers A and B cannot collide.

(B) Swimmers A and B will definitely collide some where on line AB.

(C) Swimmers A and B will definitely collide some where to the east of line AB.

(D) Swimmers A and B will definitely collide some where to the west of line AB.

34. Two Particles instantaneously at A & B respectively 4.5 meters apart are moving with uniform velocities as

shown in the figure. The former towards B at 1.5 m/sec and the latter perpendicular to AB at 1.125 m/sec.

The instant when they are nearest is:

(A) 2 sec (B) 3 sec

A'A B

B'

4.5 m(C) 4 sec (D) 1

23

25 sec

35. Ram moves with a velocity of 10 m/s in west direction. Shyam moves a direction 23° East of North. Ram is

100 m away from Shyam in direction 53° East of North of him. What should be speed of Shyam so that he

collides with Ram.

(A) 4 3 m/s (B)10 m/s (C) 12 m/s (D) none of these

36. To man running at a speed of 5 m/sec,the rain drops appear to be falling at an angle of 45° from the vertical.

If the rain drops are actually falling vertically downwards , then velocity in m/sec is

(A) 5 (B) 35 (C) 25 (D) 4

37. Raindrops are falling vertically with a velocity of 10 m/s. To a cyclist moving on a straight road the raindrops

appear to be coming with a velocity of 20 m/s. The velocity of cyclist is

(A)10 m/s (B)10 3 m/s (C) 20 m/s (D) 20 3 m/s

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38. An airplane pilot wants to fly from city A to city B which is 1000 km due north of city A. The speed of the

plane in still air is 500 km/hr. The pilot neglects the effect of the wind and directs his plane due north and

2 hours later find himself 300 km due north-east of city B. The wind velocity is

(A) 150 km/hr at 45°N of E (B) 106 km/hr at 45°N of E

(C) 150 km/he at 45°N of W (D) 106 km/hr at 45°N of W


An observer having a gun observes a remotely controlled balloon. When he first noticed the balloon, it was

at an altitude of 800 m and moving vertically upward at a constant velocity of 5 m/s. The horizontal

displacement of balloon from the observer is 1600 m. Shells fired from the gun have an initial velocity of 400

m/s at a fixed angle (sin = 3/5 and cos = 4/5). The observer having gun waits (for some time after

observing balloon) and fires so as to destroy the balloon. Assume g = 10 m/s2. Neglect air resistance.

400 m/s5m/s

Ground1600m

39. The flight time of the shell before it strikes the balloon is :

(A) 2 sec (B) 5 sec (C) 10 sec (D) 15 sec

40. The altitude of the collision above ground level is :

(A) 1075 m (B) 1200 m (C) 1250 m (D) 1325 m

41. After noticing the balloon, the time for which observer having gun waits before firing the shell is:

(A) 45 sec (B) 50 sec (C) 55 sec (D) 60 sec

42. Column-I Column-II

(A) If swimmer can swim at 5m/sec in still water and if (P) 53°

velocity of water flow is 4m/sec then angle between

direction of swimming and direction of river flow to

minimize drift.

(B) If swimmer can swim at 5m/sec in still water and (Q) 127°

velocity of flow is 3m/sec then angle between direction

of velocity of swimmer with respect to river and the

direction of river flow if swimmer crosses the river in

minimum time .

(C) If swimmer can swim at 4 m/sec and velocity of (R) 143°

flow is 3m/sec then angle of resultant velocity

(w.r.t. ground) with the direction of river flow if swimmer

swims perpendicular to flow of river.

(D) Angle between direction of fluttering of flag and (S) 90°

north if wind blows towards south west direction

with a velocity 3 2 m/sec. Man moves with a

velocity 7m/sec along west, holding flag in his hand.

Code :

(A) R S P Q

(B) S R P Q

(C) Q S P R

(D) R S Q P

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Problems on constrained motion

43. The ratio of acceleration of pulley to the acceleration of the block is (string is inextensible)

PmF

(A) 0.5 (B) 2 (C) 1 (D) None of these

44. Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the

figure.

(A) 3/2 m/s (B) 3/2 m/s (C) 1/2 m/s (D) 1/2 m/s

45. Two masses A and B are connected with two an inextensible string to write constraint relation between vA &

vB

BvA

vB

A

Student A : vA cos = v

B

Student B : vB cos = v

A

(A) A is correct, B is wrong (B) B is correct, A is wrong

(C) both are correct (D) both are wrong

46. Find velocity of ring B (vB) at the instant shown. The string is taut and inextensible :

30°

60°

v = 1m/sA

vB

A

B

(A) 1

2m/s (B)

3

4 m/s (C)

1

4 m/s (D) 1 m/s

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47. In the figure shown, the blocks A and B are connected with an inextensible string. If the block B is pulled

with a velocity of 5 m/s then it is observed that block A moves with 10 m/s. Find the angle (in degree)

shown in the diagram

A

B

10 m/s

5 m/s

(A) 60° (B) 30° (C) 45° (D) 37°

48. In the figure shown, find out the value of [assume string to be tight]

(A) tan–1(3/4) (B) tan–1(4/3) (C) tan–1(3/8) (D) None

49. System is shown in figure and wedge is moving towards left with speed 2 m/s. Then velocity of the block B

will be

(A) 3 m/s (B) 1 m/s (C) 2 m/s (D) 4 m/s

50. System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity

of cylinder is

(A) u

19 4 32

m/s (B) 13u

2m/s (C) 3u m/s (D 7u m/s

51. A block B moves with a velocity u relative to the wedge A. If the velocity of the wedge is v as shown in figure,

what is the value of so that the block B moves vertically as seen from ground.

B

u

Av

(A) cos–1u

v

(B) cos–1v

u

(C) sin–1u

v

(D) sin–1v

u

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EXERCISE-II

1. A particle is moving along the locus: y = kx (k > 0) with a constant speed 'v'. At t = 0, it is at the origin and

about to enter the first quadrant of x-y axes. At some later time t > 0, vx = vy. At this moment,

[ay – a

x] =

(A) v2/k2 (B) zero (C) –v2/k2 (D) none

2. An object is moving in the xy plane with the position as a function of time given by ˆ ˆr x(t)i y(t) j

. Point O

is at r 0

.The distance of object from O is definitely decreasing when

(A) vx> 0, vy > 0 (B) vx < 0, vy < 0 (C) xvx + yvy < 0 (D) xvx + yvy > 0

Question No. 3 to 4 (2 questions)

The following two questions refer to the following information. An ideal elastic rubber ball is dropped from a

height of about 2 meters, hits the floor and rebounds to its original height.

3. Which of the following graphs would best represent the distance above the floor versus time for the above

bouncing ball?

(A) (B) (C) (D)

4. Which of the following graphs would best represent acceleration versus time for the bouncing ball?

(A) (B) (C) (D)


An engine, approaching a tunnel at constant speed, whistles twice at interval of 10 minutes. The driver

hears the echo of the first 20 s after its sounding; while he hears the echo of the second, 16 seconds after

its sounding. [Speed of sound = 358.8 m/s]

5. The speed of the train is

(A) 2.4 m/s (B) 0.6 m/s (C) 12 m/s (D) 1.2 m/s

6. The distance of the engine from tunnel when the first whistle sounded is

(A) 360 m (B) 3.6 km (C) 1.8 km (D) 180 m

7. The distance of the engine from the tunnel when the second whistle sounded is

(A) 2.88 km (B) 3.6 km (C) 360 m (D) 288 m

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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 Vy(t = 0) = 0. The acceleration of the rocket is given by

4b

y

b

–g g t ;0 t t

a

g ;t t

where tb =

1/4g

is the time at which fuel burns out. is a positive dimensionless number ( >1 ).

8. The expression for the velocity Vy(t) valid at all times in the interval 0 < t < t

b is

(A) Vy = ( – 1)gt + 1

5t5 (B) Vy = ( – 1)gt –

1

5t5

(C) Vy = ( + 1)gt +

1

5t5 (D) V

y = ( + 1)gt –

1

5t5

9. The expression for the velocity Vy(t) valid for the time interval t > t

b is

(A) Vy = 1

5gtb + gt (B) Vy = –g(t – tb) (C) Vy = g(t – tb) (D) Vy =

4

5gtb – gt

10. The time taken for rocket to reach its maximum height is

(A) 3

5tb (B)

4

5tb (C)

1

5tb (D)

2

5tb

11. Two particles are projected simultaneously from the same point with the same speed, but different angles

of projection and . ( < )

(A) The line joining the positions of the particle at any subsequent time makes a constant angle α β

2 2

with the horizontal.

(B) The line joining the positions of the particle at any subsequent time makes a constant angle α β

2 2

with the horizontal.

(C) The magnitude of the relative velocity of the first particle with respect to the second is 2u sin α β

2

.

(D) The magnitude of the relative velocity of the first particle with respect to the second is 2u cos α β

2

.

12. A projectile thrown from ground at some angle is having velocities u and v at two points during its flight.

If u and v are perpendicular to each other then the minimum kinetic energy during the journey is [mass

of the projectile is m]

(A)

22

22

vu

vum

2

1(B)

)vu(

uv

2

m22

(C) 22

22

vu

)vu(

2

m (D)

uv

)vu(

2

m 22

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13. Two inclined planes (I) and (II) have inclination and respectively with horizontal, (where, + = 90°)

intersect each other at point O as shown in figure. A particle is projected from point A with velocity u along

a direction perpendicular to plane (I). If the particle strikes (II) perpendicularly at B, then :

(I) (II)

u

AB

O

(A) time of flight = 2u/g sin (B) time of flight = u/g sin

(C) distance OB = u2/2g sin (D) distance OB = u2/2g sin

14. A ball thrown down the incline strikes at a point on the incline 25 m below the horizontal as shown in the

figure. If the ball rises to a maximum height of 20 m above the point of projection, the angle of projection

(with horizontal x axis) is

20m

25m

Y

X

75m

(A) tan–14

3(B) tan–1

3

4(C) tan–1

3

2(D) tan–1

2

3

15. A fixed re-coilless cannon fires a shell with a speed, at the same instant a man falls from rest from point O.

The shell hits a point on the wall. Initially shell is aimed towards a point P as shown in figure. Mark the

incorrect option(s)

b

P

v0

0

O

(A) The falling man sees the shell move along straight line directed along initial velocity.

(B) Time taken to reach wall is 0 0

b

v cos

(C) For a stationary man shell will strike below P

(D) Man falls through 2 2

020

b tan1y g

2 v

till the shell hits wall.

16. Find the speed of the intersection point O of the two wires if the wires starts moving perpendicular to itself

with speed v as shown in figure.

(A) v cosec(/2) (B) v cosec() (C) v cos (/2) (D) v sec (/2)

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17. PQ is a smooth inclined plane whose angle of inclination can be varied in such a way that point Q remains

fixed & P can move on a vertical line PR. A particle slides from rest from point P. At different values of time

for descent td from P to Q is noted. The following statement is true about td:

(A) minimum value of td is 2 g

(B) td is minimum when approaches 90°

(C) td decreases continuously as is increased. (D) td first increases then decreases as is increased

18. Two small balls A & B are launched in the same vertical plane simultaneously, with same speed of 20 m/s

at t = 0. Ball A has an initial horizontal velocity and ball B has initial velocity at an angle above the line

joining A and B as shown. If the projectiles collide in mid-air at time t :

B

A

m3100

100m

•

•

20 m/s

20 m/s

(A) = 45° (B) = 60° (C) t = 20

3s (D) t =

10

3s

19. In the figure shown two boats start with different speed relative to water simultaneously. Water flow speed

is same for both the boats. Mark the incorrect statements. A and B are angles from a y-axis at which boats

are heading at initial moment.

y

FlowA

vB

vAB

(A) If vA > v

B then for reaching the other bank simultaneously

A >

B

(B) In case (A) drift of boat A greater than boat B.

(C) If vB > v

A and

A >

B , boat B reaches other bank earlier than boat A.

(D) If vB = v

A and

A >

B drift of A is less.

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EXERCISE-III1. A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At

the same instant another body passes through x = 0 moving in the positive x-direction with a constant speed.

The position of the first body is given by x1(t) after time 't' and that of the second body by x2(t) after the same

time interval. Which of the following graphs correctly describes (x1 – x2) as a function of time 't'?

[AIEEE-2008]

(A)

O

(x – x )1 2

t

(B)

O

(x – x )1 2

t

(C)

O

(x – x )1 2

t

(D)

O

(x – x )1 2

t

2. A particle is moving with velocity ),jxiy(K

where K is a constant The general equation for its path is

(A) xy = constant (B) y2 = x2 + constant

(C) y = x2 + constant (D) y2 = x + constant [AIEEE-2010]

3. Two fixed frictionless inclined planes making an angle 30° and 60° with the vertical are shown in the figure.

Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect

to B? [AIEEE-2010]

(A) Zero

(B) 4.9 ms–2 in vertical direction

(C) 4.9 ms–2 in horizontal direction

A

60°

B

30°(D) 9.8 ms–2 in vertical direction

4. An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : [AIEEE-2011]

v5.2–dt

dv

where v is the instantaneous speed. The time taken by the object, to come to rest, would be :(A) 1 s (B) 2 s (C) 4 s (D) 8 s

5. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boycan throw the same stone up to will be : [AIEEE-2012]

(A) 10 m (B) 10 2 m (C) 20 m (D) 20 2

6. A ball is dropped vertically from a height d above the ground it hits the ground and bounces up vertically to a

height d/2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the

ground as [JEE'2000 (Scr)]

(A) (B) (C) (D)

VIBRANT ACADEMY

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7. 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

[JEE' 2004 (Scr)]

(A) 110 m/s (B) 55 m/s (C) 550 m/s (D) 660 m/s

8. A small block slides without friction down an inclined plane starting from rest. Let Sn be the distance travelled

from time t = n – 1 to t = n. Then 1n

n

S

S

is [JEE' 2004 (Scr)]

(A) 2n 1

2n

(B)

2n 1

2n 1

(C)

2n 1

2n 1

(D)

2n

2n 1

9. The velocity displacement graph of a particle moving along a straight line is shown.

The most suitable acceleration-displacement graph will be

[JEE' 2005 (Scr)]

(A) (B) (C) (D)

10. A projectile is given an initial velocity of j2i m/s, where i is along the ground and j is along the vertical.

If g = 10 m/s2, the equation of its trajectory is : [IIT Main 2013]

(A) 4y = 2x – 25x2 (B) y = x – 5x2 (C) y = 2x – 5x2 (D) 4y = 2x – 5x2

11. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the

particle, to hit the ground, is n times that taken by it to reach the highest point of its path.

The relation between H, u and n is : [IIT Main 2014]

(A) g H = (n – 2)2u2 (B) 2 g H = nu2(n – 2) (C) g H = (n – 2)u2 (D) 2 g H = n2u2

12. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10m/s and

40 m/s respectively. Which of the following graph best represents the time variation of relative position of the

second stone with respect to the first ?

(Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s2)

(The figures are schematic and not drawn to scale) [IIT-JEE Main 2015]

(A)

12t(s)

8

240(y –y )m2 1

(B)

12t(s)

8

240(y –y )m2 1

t

(C)

12t(s)

240(y –y )m2 1

(D)

12t(s)

8

240(y –y )m2 1

13. A body is thrown vertically upwards. Which on the following graphs correctly represent the velocity vs time?

(A) t

(B) t

(C) t

(D)

t

[IIT-JEE Main 2017]

VIBRANT ACADEMY

unacademy



14. All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.[IIT-JEE Main 2018]

(A) time

velocity

(B) position

velocity

(C) time

distance

(D) time

position

15. Starting at time t = 0 from the origin with speed 1 ms–1, a particle follows a two-dimensional trajectory in the

x-y plane so that its coordinates are related by the equation y = 2x

2. The x and y components of its

acceleration are denoted by x and y, respectively. Then

(*A) x = 1 ms–2 implies that when the particle is at the origin, y = 1 ms–2

(*B) x = 0 implies y = 1 ms–2 at all times

(*C) at t = 0, the particle’s velocity points in the x-direction

(*D) x = 0 implies that at t = 1 s, the angle between the particle’s velocity and the x axis is 45°

[IIT-JEE Advance 2020]

VIBRANT ACADEMY

unacademy



ANSWER KEY

EXERCISE-I

1. A 2. C 3. D 4. B 5. D 6. B 7. B

8. C 9. B 10. D 11. C 12. D 13. A 14. D

15. B 16. B 17. D 18. B 19. C 20. C 21. C

22. A 23. B 24. A 25. D 26. C 27. D 28. A

29. B 30. C 31. C 32. A 33. C 34. D 35. C

36. A 37. B 38. A 39. B 40. A 41. B 42. A

Problems on constraint motion

43. A 44. A 45. A 46. D 47. A 48. D 49. C

50. D 51. B

EXERCISE-II

1. C 2. C 3. C 4. B 5. D 6. B 7. A

8. B 9. D 10. B 11. B 12. A 13. C 14. A

15. D 16. A 17. A 18. D 19. D

EXERCISE-III

1. B 2. B 3. B 4. B 5. C 6. A 7. B

8. C 9. B 10. C 11. B 12. D 13. B 14. C

15. A,B,C,D

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