Kinematics Physics Problems

Motion in one dimensions

Q.1

Q.2

Q.3

Q.4

Q.5

Q.6

Q.7

Q.8

Q.9

. A runner completes one round of a circular path of radius r in 40 seconds. His displacement after 2 minutes

20 seconds will be

[1] zero [2] 2 r [3] 2r [4] 7 r

. An old man goes for morning walk on a semicircular track of radius 40 m; if he starts from one end of the track and

reaches to other end, the distance covered by the man displacement will respectively be

[1] 126 m, 80 m [2] 80 m, 126 m [3] 80 m, 252 m [4] 252 m, 80 m

. A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacement is

[1] 2 2

[2] 2 2

[3] 2

[4] 2

. A passenger travels along a straight line with velocity v1 for first half time and with velocity v

2 for next half time, then

the mean velocity v is given by

[1] 1 2v v

v2

[2] 1 2v v v [3] 2

1

vv

v [4] 1 2

2 1 1v v v

. A car covers a distance of 2 km in 2.5 minute, if it covers half of the distance with speed 40 km/hr, the rest distanceit will cover with speed

[1] 56 km/hr [2] 60 km/hr [3] 50 km/hr [4] 48 km/hr

. A bicyclist encounters a series of hills. Uphill speed is always v1 and downhill speed is always v

2. The total

distance travelled is , with uphill and downhill portions of equal length. cyclist's average speed is

[1] 1

2

vv [2]

2

1

vv [3]

1 2

1 2

v vv v [4]

1 2

1 2

2v vv v

. A motor car covers 13

rd part of total distance with 1v 10km / hr , second 13

rd part with 2v 20 km/hr and

rest 13

rd part with 3v 60km / hr . What is the average speed of the car?

[1] 18 km/hr [2] 45 km/hr [3] 6 km/hr [4] 22.5 km/hr

. The displacement-time graph for the two particles A and B are straight lines inclined at angles 300 and 600 with the

time axis. The ratio of the velocities of A to B will be

[1] 1 : 2 [2] 1: 3 [3] 3 :1 [4] 1 : 3

. The velocity-time graph of a body is shown in figure. The displacement covered by the ody in 8 seconds is

[1] 10 m

[2] 9 m

[3] 24 m

[4] 30 m

(Sec)t1 2 3 4

5 6 7 8

64

2

-6

(m/s

ec)

p p

p

p

p

p

+= = = = +

+ +

= =

=

l

EXERCISE # 1


Q.10

Q.11

Q.12

Q.13

Q.14

Q.15

Q.16

Q.17

. The variation of velocity of a particle moving along straight line is shown in figure. The distance traversed by thebody in 4 seconds is

[1] 70 m

[2] 60 m

[3] 40 m

[4] 55 m

. The displacement y (in metres) of a body varies with t me (in seconds) according to the equation

22y t 16t 2

3. How long does the body come to rest?

[1] 8 seconds [2] 10 seconds [3] 12 seconds [4] 14 seconds

. If y denotes the displacement and t denotes the time and the displacement is given by y asin t , the velocity

of the particle is

[1] acos t [2] a cos t [3] a cos t [4] a cos t

. A truck travelling due to North at 20 m/s turns East and travels at the same speed. The change in its velocity is

[1] 20 2 m/ sNorth East [2] 20 2 m/ sSouth East

[3] 40 2 m/ sNorth East [4] 20 2 m/ sNorth West

. Which one of the following equations represent the motion of a body with finite constant acceleration. In these

equations y denotes the displacement of the body at time t and a,b and c are the constant of the motion

[1] y = t

a + bt [2] y at [3] 2y at bt [4] 2 3y at bt ct

. A car moving at 12 m/s due east attains a speed 16 m/s towards north in 4 seconds. The magnitude of its average

acceleration in m/s2 is

[1] 1 m/s2 [2] 3 m/s2 [3] 5 m/s2 [4] 7 m/s2

. Adjacent graph shows the variation of velocity of a rocket with time. Find the time of burning of fuel from the graph

[1] 10 sec

[2] 110 sec

[3] 120 sec

[4] cannot be estimated from the graph

. The adjoining curve represents the velocity-time graph of a particle, its acceleration values along OA, AB and BC

in metre/sec2 are respectively

[1] 1,0,–0.5

[2] 1,0,0.5

[3] 1,1,0.5

[4] 1,0.5,0

y

x

1 2 3 4O

10

20

velo

city

(m/s

ec)

Time (sec)

A B

2010 30 40C

5 –

10 –

velo

city

inm

/sec

Time in sec

= − + +

=

−( )

− −

− −

= = + = + +

→

w

w w w ww

w

Time (second)Vel

ocity

in m

/s

110

120

1 00 0

10


Q.18

Q.19.

Q.20.

Q.21.

Q.22.

Q.23.

Q.24.

Q.25.

Q.26.

Q.27.

. A car travels first 1/3 of the distance AB at 30 km/hr next 1/3 of the distance at 40 km/hr, last 1/3 of the distanceat 24 km/hr. Its average speed in km/hr for the whole jouney is

[1] 40 [2] 35 [3] 30 [4] 28

A particle travels A to M along a straight line with a velocity of 8 m/s and M to A with a velocity of 2 m/s, then theaverage velocity for the whole journey is

[1] 3.2 m/s [2] –5 m/s [3] –3.2 m/s [4] 0 m/s

An object will continue accelerating untill

[1] the resultant force on it begins to decrease

[2] the velocity changes direction

[3] the resultant force on it is zero

[4] the resultant force is at right angles to its direction of motion

A girl walks along an east-west street, and a graph of her displacement from home is as shown in figure. Her

average velocity for the whole time intervals is

[1] zero

[2] 6 m/min

[3] 11 m/min

[4] 15 m/min

The uniform motion in the following acceleration time is

[1] AB

[2] BC

[3] CD

[4] DE

The displacement-time relationship for a particle is given by 20 1 2x a a t a t . The acceleration of the particle is

[1] 0a [2] 1a [3] 2a [4] 22a

A particle travels for 40 seconds under the influence of a constant force. If the distance travelled by the particle isS

1 in the first twenty seconds and S

2 in the next twenty seconds, then

[1] S2 = S

1[2] S

2 = 2S

1[3] S

2 = 3S

1[4] S

2 = 4S

1

A particle moves with constant acceleration for 6 seconds after starting from rest. The distance travelled during

the consecutive 2 seconds interval are in the ratio

[1] 1 : 1 : 1 [2] 1 : 2 : 3 [3] 1 : 3 : 5 [4] 1 : 5 : 9

A body having initial velocity u is moving with uniform acceleration a. The distance covered by it in nth second is

[1] a

u 2n 12

[2] a

u 2n 12

[3] a

u 2n 12

[4] a

u 2n 12

A ball is thrown upward and reaches a height of 64 feet, its initial velocity should be (g = 32 ft/sec2)

[1] 64 ft/sec [2] 72 ft/sec [3] 32 ft/sec [4] 4096 ft/sec

distance east(m)

= + +

( )+ + ( )− − ( )− + ( )+ −

t

B

AC

5 10 15 20

min

0

10203040

–30

E

DC

BA10

t

8642

5

10

15

a(m/s2)

-5


Q.28.

Q.29.

Q.30.

Q.31.

Q.32.

Q.33.

Q.34.

Q.35.

Q.36.

Q.37.

Q.38.

Q.39.

Two bodies of different masses ma and m

b are dropped from two different heights, viz a and b. The ratio of times

taken by the two to drop through these distance is

[1] a : b [2] a

b

m b:

m a [3] a : b [4] 2 2a :b

A stone weighing 10 kg is dropped from a cliff in a high wind. The wind exerts a steady horizontal force of 50 N on

the stone as it falls. The path that the stone follows will be

[1] A parabola [2] An ellipse

[3] A more complicated path [4] A straight line

A body thrown up with a finite speed is caught back after 4 sec. The speed of the body with which it is thrown

up is

[1] 10 m/sec [2] 20 m/sec [3] 30 m/sec [4] 40 m/sec

A ball is dropped from certain height on a glass floor so that it rebounds elastically to the same height. If the

process continues, the velocity-time graph for such a motion would be

[1] [2] [3] [4]

A stone is thrown vertically upwards with an initial velocity of 30 m/s. The time taken for the stone to rise to itsmaximum height is

[1] 0.326 s [2] 3.26 s [3] 30.6 s [4] 3.06 s

A body is thrown upward and reaches its maximum height. At that position

[1] its velocity is zero and its acceleration is also zero

[2] its velocity is zero but its acceleration is maximum

[3] its acceleration is minimum

[4] its velocity is zero and its acceleration is the acceleration due to gravity

The initial velocity of a particle (at t = 0) is u and the acceleration of particle at time t is given by

f = at. Where a is a constant which of the following relation for velocity v of particle after time t is true?

[1] v = u + at2 [2] v = u + at2/2 [3] v = u + at [4] none of these

A man is walking on a road with a velocity 3 km/hr. Suddenly rain starts falling. The velocity of rain is

10 km/hr in vertically downward direction. The relative velocity of the rain is

[1] 13 km/ hr [2] 7 km/ hr [3] 109 km /hr [4] 13 km/hr

A boat P is moving at 40 km/hr and another boat Q is moving at 20 km/hr. Which one of the following is not apossible value for their relative velocity


The position of a body with respect to time is given b x = 4t3 – 6t2 + 20 t + 12. Acceleration at

t = 0 will be

[1] –12 units [2] 12 units [3] 24 units [4] –24 units

A body travels 200 cm in the first two seconds and 220 cm in the next four second. The velocity at the end of the

seventh second from the start will be

[1] 10 cm/s [2] 5 cm/s [3] 15 cm/s [4] 20 cm/sA man standing on a road hold his umbrella at 300 with the vertical to keep the rain away. He throws the umbrellaand starts running at 10 km/h. He finds that raindrops are hitting his head vertically, the speed of rain drop withrespect to the road will be

[1] 10 km/h [2] 20 km/h [3] 30 km/h [4] 40 km/h

T 2TT 2T

V

tt

V

T 2TT 2T

tt

→→→→


Q.40.

Q.41.

Q.42.

Q.43.

Q.44.

Q.45.

Q.46.

Q.47.

Q.48.

Q.49

Q.50

Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ans.Qus. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Ans.Qus. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45Ans.Qus. 46 47 48 49 50Ans.

ANSWER KEY EXERCISE # 1

The linear momentum of a body is p. The linear momentum p varies with time. The equation for variation isp = a + bt2 where a and b are constants. The effective force acting on the body is

[1] proportional to t2 [2] constant [3] proportional to t [4] inversely proportional to t

The acceleration of a particle increases linearly as bt with time. If the particle starts from v0 as initial velocity then

the distance travelled in t seconds will be

[1] 3

0

1v t bt

6[2]

20

1v t bt

6[3]

30

1v t bt

6[4]

30

1v t bt

2A particle has velocity given by v = 20 + 0.1 t2 then it has

[1] uniform acceleration [2] uniform retardation

[3] non uniform acceleration [4] zero acceleration

A body starting from rest and has uniform acceleration 8 m/sec2. The distance travelled by it in 5th second will be

[1] 36 m [2] 40 m [3] 100 m [4] 200 m

A body starts from rest, the ratio of distances travelled by the body during 3rd and 4th seconds is

[1] 7/5 [2] 5/7 [3] 7/3 [4] 3/7

A body sliding on a smooth inclined plane requires 4 sec to reach the bottom after starting from rest at the top.How much time does it take to cover one fourth the distance starting from the top

[1] 1 sec [2] 2 sec [3] 0.4 sec [4] 1.6 sec

The initial velocity of a particle is 10 m/sec and its retardation is 2 m/sec2. The distance covered in the fifth second

of the motion will be

[1] 1 m [2] 19 m [3] 50 m [4] 75 m

A particle is moving east-wards with a velocity of 5m/sec. In 10 seconds its velocity changes to 5m/sec north-wards. The average acceleration during this time is

[1] 21 m/ sec

2 in N-W direction [2] 21 m/ sec

2 in the N-E direction

[3] 12 m/sec2 in N-W direction [4] 1

2 m/sec2 towards east

A ship of mass 3 x 107 kg initially at rest, is pulled by a force of 5 x 104 N through a distance of 3m. Assuming thatthe resistance due to water is negligible, the speed of the ship is

[1] 1.5 m/sec [2] 60 m/sec [3] 0.1 m/sec [4] 5 m/sec

A particle moves with a constant acceleration such tha in the successive time intervals t1 , t

2 and t

3 its

average velocities are v1, v

2 and v

3. The ratio of v

1 – v

2 and v

2 – v

3 is

[1] 1 2 2 3t t : t t [2] 1 2 2 3t t : t t [3] 1 2 2 3t t : t t [4] t1 – t

2 : t

2 – t

3

A car travels from place A to the place B at 20 km/hou and returns at 30 km/hour. The average speedof the car for the whole journey is

[1] 25 km/hour [2] 24 km/hour [3] 50 km/hour [4] 5 km/hour

3 1 1 1 2 4 1 4 2 4 3 3 2 3 3

1 1 3 4 3 1 1 4 3 3 4 1 3 4 2

3 4 4 2 3 1 1 1 2 3 1 3 1 2 2

1 1 3 2 2

+ − − +

− + + + − −


Q.1

Q.2

Q.3

Q.4

Q.5

Q.6

Q.7

Q.8

Q.9

The velocity- time graph of a l inear mot ion is shown be ow. The displacement from the or igin after

8 seconds is

1 2 3 4

5 6 7 8

-2

-4

0

2

4

t(sec)um

/s

[1] 18 m [2] 16 m [3] 6 m [4] 6 cm

A train is moving in the north at a speed 10 m/sec. I length is 150 m. A parrot is flying parallel to

the train in the south with a speed of 5 m/s. The tim taken by the parrot to cross the train will be

[1] 12 sec [2] 8 sec [3] 15 sec [4] 10 sec

A particle is moving in a plane with velocity given by 0u u i a cos t j , where i and j are unit vectors

along x and y axes respectively. If particle is at the origin at t = 0. Calculate the trajectory of the particle

[1] 0u

y asinx [2]

0

xy asin

u [3] 0u1

y .sina x [4]

0

1 xy .sin

a u

In the following velocity-time graph of a body, the distance and displacement travelled by the body in 5

second in meters will be

1 2 3

40

30

20

10

0

-10

-20

-30

4 5 t(sec)

[1] 70, 110 [2] 110, 70 [3] 40, 70 [4] 90, 50

A runner completes one round of a circular path of rad s r in 40 sec. His displacement after 2 minutes

20 sec. will be -

[1] zero [2] 2 r [3] 2r [4] 7 r

The displacement is given by x = 2t2 + t + 5, the acceleration at t = 5 sec will be

[1] 8 m/s2 [2] 12 m/s2 [3] 15 m/s2 [4] 4 m/s2

A par t ic le moves along the x-axis in such a way that i s x-coordinate var ies w ith t ime as

x = 2 – 5t + 6t2. The initial velocity and accleration of particle will espectively be

[1] –5 m/s, 12 m/s [2] 5 m/s, –12 m/s [3] –5 m/s, –12 m/s [4] 5 m/s, 12 m/s

Two trains each of length 50 m, are approaching each other on parallel rails. Their velocities are 10 m/s and

15 m/s. They will cross each other in

[1] 2 sec [2] 4 sec [3] 10 sec [4] 6 sec

A car travels a distance of 2000m. If the first half istance is covered at 40 km/hour and the second

half at velocity v and if the average velocity is 48 k /hour then the value of v is

[1] 56 km/hour [2] 60 km/hour [3] 50 km/hour [4] 48 km/hour

( )= + ω ω

= ω

ω=

= ω

ω=

π π

EXERCISE # 2


Q.10

Q.11

Q.12

Q.13

Q.14

Q.15

Q.16

Q.17

Q.18

The following figures show some velocity V versus time t curves. But only some of these can be realisedin practice. These are

t

V

t

V

t

V

t

V

(a) (b) (c) (d)

[1] Only a,b and d [2] only a,b,c [3] only b and c [4] all of them

At an instant t, the coordinates of a particle x = at2, y = bt2 and z = 0, then its velocity at the instant t will be

[1] t 2 2t a b [2] 2t 2 2t a b [3] 2 2a b [4] 2 2 22t a b

Figure shows the position of a particle moving on the -axis as a function time

[1] the particle has come to rest 6 times

[2] the maximum speed is at t = 6 sec

[3] the velocity remains positive for t = 0 to t = 6 sec

[4] the average velocity for the total period show in egative

A rocket is projected vertically upwards and its time locity graph is shown in the figure. The maximumheight attained by the rocket is

20 t(sec)120V

(M/sec)

1000

[1] 1 km [2] 10 km [3] 100 km [4] 60 km

A stone is dropped into a well and the sound of impact of stone on the water is heard after 2.056 sec

of the release of stone fro the top. If acceleration e to gravity is 980 cm/sec2 and velocity of sound

in air is 350 m/s, calculate the depth of the well

[1] 1.96 m [2] 19.6 m [3] 6.91 m [4] 69.1 m

A body is dropped from a height h under acceleration d to gravity g. If t1 and t

2 are time intervals for

its fall for first half and the second half distance, e relation between them is

[1] t1 = t

2[2] t

1 = 2t

2[3] t

1 = 2.414 t

2[4] t

1 = 4t

2

A rocket is launched from the earth surface so that it has an acceleration of 19.6 m/s2. If its engine

is switched off after 5 seconds of its launch, then th maximum height attained by the rocket will be

[1] 245 m [2] 490 m [3] 980 m [4] 735 m

If the relation between distance x and time t is denot by 2t x x where and are constant

quantities, the deceleration of the particle is

[1] 32 v [2] 3v [3] 32 v [4] 2 32 v

A particle is moving so that its displacements is given as 3 2s t 6t 3t 4 meter. Its velocity at the

instant when its acceleration is zero will be

[1] 3 m/s [2] –12 m/s [3] 42 m/s [4] –9 m/s

O O O O

= + = + + +

= α + β α β

α β αβ β

= − + +

642

10

20

t (sec)

Dis

plac

emen

t


Q.19

Q.20

Q.21

Q.22

Q.23

Q.24

Q.25

Q.26

Q.27

A car starts from rest and has an acceleration a t . A truck is moving with a uniform velocity of

4 m/s. At what distance will the car overtake the tru ? (at t = 0 both start their motion in the same

direction from the same position)

[1] 16 m [2] 8 m [3] 32 m [4] 4 m

An object is released from some height. Exactly after one second, another object is released from the

same height. The distance between the two objects exa ly after 2 secodns of the release of secondobject will be

[1] 4.9 m [2] 9.8 m [3] 19.6 m [4] 24.5 m

A ball is thrown from the ground with a velocity of 80 ft/sec. Then the ball will be at a height of 96 feet

above the ground after time

[1] 2 and 3 sec [2] only 3 sec [3] only 2 sec [4] 1 and 2 sec

A man standing on the edge of a cliff throws a stone straight up with initial speed u and then throws

another stone straight down with same initial speed u rom the same position. Find the ratio of speeds,the stone would have attained when they hit the ground at the base of the cliff?

[1] 2 : 1 [2] 1 : 2 [3] 1 : 1 [4] 3 : 1

A stone is dropped from a bridge and it reaches the gr nd in 4 seconds. The height of the bridge is

[1] 78.4 m [2] 64 m [3] 260 m [4] 2000 m

A stone is dropped from the top of a tower and it stri s with 3 km/hr against the ground. Another stone

is thrown vertically downwards from the same top of th tower with a velocity 4 km/hr. Its velocity when

it strikes the ground will be

[1] 7.0 km/hr [2] 5.0 km/hr [3] 3.5 km/hr [4] 4.0 km/hr

A stone is thrown vertically upwards from the top of a tower with a velocity u and it reaches the ground

with a velocity 3u. The height of the tower is

[1] 23u

g [2] 24u

g [3] 26u

g [4] 29u

g

The displacement of a particle as a function of time i shown in fig. The fig. indicates that

0 1 2 3 4 x

Dis

tanc

e

y

Time

[1] the particle starts with a certain velocity, but the motion is retarded and finally the particle stops

[2] the velocity of particle is constant throught

[3] the acceleration of the particle is constant throughout

[4] the particle starts with a constant velocity, the tion is accelerated and finally the particle moveswith another constant velocity.

The acceleration of a par t ic le, star t ing from rest , va ies with t ime according to the relat iona = kt + c. Then the velocity v of the particle after a time t will be

[1] 22kt ct [2] 21

kt ct2

[3] 2kt ct [4] 21

kt ct2

=

+ + + ( )+


Q.28

Q.29

Q.30

Q.31

Q.32

Q.33

Q.34

The velocity of a particle moving in the positive dire ion of x-axis varies as v x where is positive

constant. Assuming that at the moment t = 0, the particle was located at x = 0 the value of time dependenceof the velocity and the acceleration of the particle

[1] 2 2

t 1,

2 2[2]

2 2t,

2 2[3] 2

2t, 2

2[4] None of these

Three points are located at the vertices of an equilateral triangle whose side equals a. They all startmoving simultaneously with velocity V constant in magnitude. With the first point heading continuously

for the second, the second for the third and the third for the first. How soon will the points coverage?

[1] 3Va

[2] 2a3V

[3] a

3V[4]

aV

Two bodies of masses m1 and m

2 are dropped from height h

1 and h

2 respectively. They reach the ground

after time t1 and t

2 respectively. Which of the following relation is correct

[1]

1/ 2

1 1

2 2

t ht h [2]

1 1

2 2

t ht h [3]

1/2

1 1

2 2

t mt m [4]

1 1

2 2

t mt m

Which of the following statements is wrong about a bal thrown vertically up?

[a] it is moving with constant acceleration

[b] it may have different velocities at the same posit n

[c] it may have two positions at the same time

[d] the angular momentum of the particle about origin emains conserved

[1] c only [2] c, d [3] b, c, d [4] a, b, c and d

A particle is projected vertically upwards and it reaches the maximum height H in time T seconds. The

height of the particle at any time t will be

[1] 2

g t T [2] 21

H g t T2

[3] 21

g t T2

[4] H g t T

A rocket is fired vertically upwards such that its engine takes 10 seconds in exploding fully. Its velocitytime curve is shown in the figure. The height reached by the rocket is

10 20 30 40 50Time (in sec)

V elo

city i

nm

/s 1000

500

[1] 20 kms [2] 40 kms [3] 400 kms [4] 1000 kms

If the displacement of a particle varies with time according to the relation K

x [1 exp bt ]b

, then the

velocity (V) of the particle is

[1] V K exp bt [2] K

V exp btb

[3] )btexp(b

KV

2

[4] 2

KV exp bt

b

= α α

α αα α

α α

=

=

=

=

( )− ( )− − ( )− ( )− −

( )= − −

( )= − ( )= − −= ( )= −


Q.35

Q.36

Q.37

Q.38

Q.39

Q.40

Q.41

Q.42

Q.43

Q.44

Q.45

If velocity of a particle is given by 2V 10 2t m/ s . The average acceleration between 2 and 5 s is

[1] 2 m/s2 [2] 4 m/s2 [3] 12 m/s2 [4] 14 m/s2

A body of mass 3 kg falls from the multistoreyed building 100 m high and buries itself 2 meters deep

in the sand. The time of penetration will be

[1] 9 sec. [2] 0.9 sec. [3] 0.09 sec. [4] 10 sec.

A body travelling with uniform acceleration crosses tw points A and B with velocities 20 m/sec and

30 m/sec respectively. Then the speed of the body at d-point of A and B is

[1] 25 m/sec [2] 25.5 m/sec [3] 24 m/sec [4] 10 6 m/sec

Two mirrors, mounted vertically, are made to move towards each other with a speed v m/s each. A particle that can

bounce back between the two mirrors starts from one mirror when the mirrors are d meters aprat. On reaching thesecond mirror, it bounces back and so on. If the particle keeps on travelling at a constant speed of 3 v m/s, how

many trips can it make before the mirrors run into each other and what total distance does it cover

[1] ,5.1d [2] ,1.5d [3] 0,6.1d [4] 0,1.6d

Two trains each having a speed of 30 km/hour are headed at each other on the same straight track. Abird that can fly at 60 km/hour flies off from one tra when they are 60 km apart and heads directly for

the other train. On reaching the other train it flies directly back to the first, and so fourth then the total

distance travelling by the bird is

[1] 40 km [2] 60 km [3] 80 km [4] 100 km

The distance covered by the body in time 't' is propor onal to the square of the time 't'. The acceleration

of the body is

[1] increasing [2] decreasing [3] zero [4] constant

If the displacement of a particle varies with time as x t 7 , the

[1] velocity of the particle is inversely porportional to t [2] velocity of the particle is proportional to t

[3] velocity of the particle is proportional to t [4] the particle moves with a constant acceleration

Between two stations a train accelerates uniformly at rst, then moves with constant speed and finally

retards uniformly. If the ratios of time taken are 1 8 : 1 and the greatest speed is 60 km/hour. Thenthe average speed over the whole journey


A car accelerates from rest at a constant rate for some time after which it decelerates at a constant

rate to come to rest. The maximum velocity V reached if t al time taken (t seconds) is given by

[1] V t [2]

2

V t [3]

2

V t [4] V t

The distance x travelled by the car in above problem in time 't' is given by

[1]

2tx

2 [2] 2x t [3]

2x t [4]

2tx

2

A ball is thrown vertically upwards with a velocity of 30 m/s. If the acceleration due to gravity is10 m/s2, what will be the distance travelled by it in the las second of motion.

[1] 5 m [2] 10 m [3] 25 m [4] 30 m

= +

∞ ∞

= +

α

β

αβ=

α −β

β= α − β

α= α + β

αβ= α +β

αβ= α −β

αβ= α + β

α + β= α −β

αβ= α +β


Q.46

Q.47

Q.48

Q.49

Q.50

Q.51

Q.52

Q.53

Q.54

Q.55

Q.56

Q.57

Q.58

Q.59

Two balls are dropped from different heights. One ball is dropped 2 sec after the other but they bothstrike the griound at the same time, 3 sec after the f st is dropped. The difference in the heights at

which they were dropped is

[1] 7.8 m [2] 78 m [3] 15.6 m [4] 39.2 m

If a body travels half its total path in the last seco of its fall from rest then the time and height of its fall are

[1] 3.41 sec, 57 m [2] 4.31 sec, 57 m [3] 1.34 sec, 57 m [4] 3.14 sec, 75 m

From the foot of a tower 90 m high, a stone is thrown so as to reach the top of the tower. Two second

later another stone is dropped from the top of the tower. The two stones will meet at

[1] 83.6 m [2] 38.6 m [3] 63.8 m [4] 68.3 m

Two bodies are thrown vertically upward, with the same initial velocity of 98 m/s but 4 sec apart. Howlong after the first one is thrown will they meet?

[1] 10 sec [2] 11 sec [3] 12 sec [4] 13 sec

A ball is thrown vertically upwards from the top of a wer with a velocity of 10 m/sec. If the ball falls

on the ground after 5 seconds, the height of the tower will be

[1] 25 m [2] 50 m [3] 75 m [4] 100 m

In the above question, what height above the tower will the ball attain?

[1] 5 m [2] 5 m [3] 5 2 m [4] 10 m

In the above question, the total distance travelled by the ball before it returns to the ground is

[1] 85 m [2] 75 m [3] 100 m [4] 175 m

In the above question, in what time will it reach the aximum height

[1] 1 sec [2] 2 sec [3] 2 sec [4] 1/ 2 sec

In the above question, with what velocity will the bal strike the ground

[1] zero [2] 40 m/s [3] 10 m/s [4] 60 m/s

A stone is dropped from the top of the tower and trave 24.5 m in the last second of its journey. Theheight of the tower is

[1] 44.1 m [2] 49 m [3] 78.4 m [4] 72 m

Two balls are dropped from the same point after an int val of 1 s. If acceleration due to gravity is 10m/s2, what will be the separation 3 seconds after the release of first ball?

[1] 5 m [2] 10 m [3] 25 m [4] 30 m

Two balls of equal masses are thrown upwards along the same vertical direction at an interval of 2 seconds.

With the same initial velocity of 39.2 m/sec. Then these collide at a height of

[1] 117.6 m [2] 73.5 m [3] 196.0 m [4] 44.1 m

The speed v of a particle movign along a straight line, when it is at a distance x from a fixed point onthe line is given by v2 = 108 x – 9x2 . Then magnitude of its acceleration when it is at a istance 3 metre

from the fixed point is

[1] 9 m/s2 [2] 18 m/s2 [3] 27 m/s2 [4] None of these

A body is thrown up in a lift with a velocity u relati to the lift and the time of flight is found to be 't'.The acceleration with which the lift is moving up will be

[1] u gt

t[2]

u gtt

[3] 2u gt

t[4]

2u gtt

− + − +


Q.60

Q.61

Q.62

Q.63

Q.64

Q.65

Q.66

Q.67

Q.68

Q.69

A body dropped from the top of a tower covers 7/16 of e total height in the last second of its fall. Thetime of fall is

[1] 2 sec [2] 4 sec [3] 1 sec [4] 50

sec7

A person standing on the roof of a house of height h throws a particle vertically downwards and other particlein a horizontal direction with the same speed u. The tio of speeds of the particles on reaching the earth is

[1] 2gh :u [2] 1 : 2 [3] 2 :1 [4] 1 : 1

In the above question, the ratio of vertical component of the velocities will be

[1] one [2] more than one [3] less than one [4] will depend on mass

In the above question the first particle instead of being thrown downwards, is thrown upwards with the

same velocity. The ratio of the velocities of the par icles on reaching the earth, will be

[1] 1 : 1 [2] 2 :1 [3] 2 : 1 [4] 1 : 4

Juggler keeps on moving four balls in the air continuo ly such that each ball attains 20 m height. Whenthe first ball leaves his hand, the position of the ot r balls ( in metre height) will be

[1] 10, 20, 10 [2] 15, 20, 15 [3] 5, 51, 20 [4] 5, 10, 20

The retardation of a motor boat after its engine is sw ched off, is given by dvdt

= – kv30, where k is a

constant and v0 is its velocity at the time of shutting off of the en ne. The velocity of the motor boat

after time t will be

[1] 0

20

v

2v kt 1 [2] kt0v e [3]

0v2

[4] v0

A par t ic le moves w ith constant speed v along a regular hexagon ABCDEF in same order(ie., A to B, B to C, C to D, D to E, E to F, F to A.. ) Then magnitude of average velocity for its motionfrom A to C

[1] V [2] V/2 [3] 3V / 2 [4] None of these

The acceleration (a) of moving particle varies with displacement according to the following relation 2a x 3x .

Then correct relation between velocity and displacemen is (where C = constant)

[1] 3 2x 3x

V C3 2

[2]3 22

V x 3x C3

[3] 3 22

V x 3x C3 [4] V = 2x + 3

If a point moves in a straight line in such a manner t t its retardation is proportional to its speed, thedistance covered (x) is assosciated with speed (V) is

[1] x V [2] 2x V [3] 3x V [4] x V

A ball is dropped from a height of 20 m and rebounds with a velocity which is 3/4th of the velocity with whichit hits the ground. What is the time interval between the first and second bounces (g = 10 m/s2)

[1] 3 sec [2] 4 sec [3] 5 sec [4] 6 sec

+−

= +

= + + = + +

= + +

∝ ∝ ∝ ∝ −


Q.70

Q.71

Q.72

Q.73

Q.74

Q.75

Q.76

Q.77

Q.78

Q.79

Q.80

A river is flowing from west to east at a speed of 5 metres/minute. A man on the south bank of the

river, capable of swimming at 10 metres/min. in still ater, wants to swim across the river in shortest

time. He should swim in a direction

[1] due north [2] 300 east of north [3] 300 west of north [4] 600 east of north

A particle moves along a circle with a uniform speed v After it has made an angle of 600, the change in itsspeed will be

[1] v 2 [2] v

2[3] v 3 [4] 0

A boat moves relative to water a velocity which is 1/n times the river flow velocity. At what angle to thestream direction must be boat move to minimize drifting?

[1] / 2 [2] 1 1sin

n[3]

1sin 1/n2

[4] 1sin 1/ n

2

A particle moves with a v in a horizontal circular pat The change in its velocity for covering 600 will be

[1] v 2 [2] v / 2 [3] v 3 [4] v

A car A is goving north-east at 80 km/hr. and antoher ar 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 such that tan is

[1] 1/7 [2] 3/4 [3] 4/3 [4] 3/5

The motion of particle is defined by x acos t and y asin t . The acceleration of particle is

[1] a [2] 2a [3] –a 2 [4] 2 2a

A boat man could row his boat with a speed 10 m/sec. He wants to take his boat from P to a point Q justopposite on the other bank of the river flowing at a s ed 4 m/sec. He should row his boat

[1] at right angle to the stream

[2] at an angle of 1sin 2 / 5 with PQ up the stream

[3] at an angle of 1sin 2 / 5 with PQ down the stream

Q

P

V =4m/ss

[4] at an angle of 1cos 2 / 5 with PQ down the stream

A particle is executing a circular motion of radius R th a uniform speed v. After completing half the circle,the change in velocity and in speed will be respectively

[1] zero, zero [2] 2 v, zero [3] 2 v, 2 v [4] zero, 2 v

A balloon is at a height of 81 metres and is ascending upwards with a velocity of 12 m/s. A body of 2 kgweight is dropped from it. If g = 10 m/s2, the body will reach the surface of the earth in

[1] 1.5 sec [2] 4.025 sec [3] 5.4 sec [4] 6.75 sec

If the position vector of a particle is kj4it3r , the particle will be

[1] moving with uniform velocity [2] stationary

[3] moving with uniform acceleration [4] insufficient data

A bullet loses 1

20 of its velocity in passing through a plank. The least number of planks required to stop the

bullet is -

[1] 10 [2] 11 [3] 12 [4] 23

π −

( )−π+ ( )−π

−

α α

= ω = ω

ω ω ω ω

( )−

( )−

( )−

+−=→


Q.81

Q.82

Q.83

Q.84

Q.85

Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ans.Qus. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Ans.Qus. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45Ans.Qus. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60Ans.Qus. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75Ans.

Qus. 76 77 78 79 80 81 82 83 84 85Ans.

The motion of a body falling from rest in a resisting medium is described by the equation dva bv

dt, where

a and b are constants. The velocity at any time t is -

[1] bt

t

av (1 e )

b[2]

btt

bv e

a[3]

btt

av (1 e )

b[4]

btt

bv e

a

A ball is thrown vertically upwards. It was observed a a height h twice with a time interval t. The initial

velocity of the ball is -

[1] 2 28gh g ( t) [2] 2

g t8gh

2[3]

2 218gh g ( t)

2[4] 2 28gh 4g ( t)

A stone falls freely from a point O. It passes through he points P, Q, R ....... such that OP, OQ, OR,.... are

in geometric progression. Then velocities of stone at P, Q, R.... are in -

[1] arithmetic progression [2] geometric progression

[3] harmonic progression [4] logarithmic mean

A ship of mass 3 × 107 kg, initially at rest, is pulled by a force of 5 × 104N through a distance of 3m.

Assuming that the resistance due to water is negligibl the speed of the ship is -

[1] 1.5 ms–1 [2] 60 ms–1 [3] 0.1 ms–1 [4] 5 ms–1

An elevator whose floor to ceilling distance is is ascending with uniform acceleration it. At some in ant

(say t = 0), a loose bolt drops from its ceiling. The time taken by the bolt to hit the floor is -

[1] 2

g a [2] 2g [3]

2g a [4]

2

a

3 4 2 2 1 4 1 2 2 1 2 1 4 2 3

4 1 4 1 4 1 3 1 2 2 1 2 2 2 1

1 2 1 1 4 3 2 2 2 4 4 2 4 4 3

4 1 1 3 3 2 1 1 2 1 3 2 3 3 2

4 2 1 2 1 3 2 4 1 1 4 3 4 1 3

2 2 3 1 2 1 3 2 3 3

= −

−= − −= −= + =

∆

+ ∆∆ +

+ ∆ + ∆

− +

l

l l l l

ANSWER KEY EXERCISE # 2


Q.1

[CPMT-1990]

Q.2

[CET Karnataka-94]

Q.3

Q.4[AFMC-94]

Q.5

[AFMC-94; CBSE-94]

Q.6

[RPMT-94]

Q.7

[RPMT-94]

Q.8

[EAMCET-95]

The displacement time graph for two particles A and B are straight lines inclined at angles of 300 and 600 with the

time axis. The ratio of velocity of A BV : V is

[1] 1 : 2 [2] 1: 3

[3] 3 :1 [4] 1 : 3

An elevator car, whose floor to celling distance is equal to 2.7 m, starts ascending with constant acceleration of

1.2 ms-2. 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is

[1] 0.54 s [2] 6 s [3] 0.7 s [4] 1s

A body 'A' is dropped vertically from the top of a tower. If another identical body 'B' is projected thrown from thesame point at the same instant, then

[1] 'A' will reach the ground earlier than 'B'

[2] 'B' will reach the ground earlier than 'A'

[3] Both 'A' and 'B' will reach the ground simultaneously

[4] none of these

A body is dropped from the top of a tower with zero velocity and reaches ground in 4 seconds. The height of thetower is about [g = 10 m/s2]

[1] 20 m [2] 40 m [3] 80 m [4] 160 m

The time displacement graph of a moving particle is shown as the instantaneous velocity is negative of the point

[1] D

[2] F

[3] C

[4] E

A balloon is at a height of 81 m and is ascending upwards with a velocity of 12 m/s. A body of 2 kg weight isdropped from it. If g = 10 m/s2, the body will reach the surface of the earth in

[1] 1.5 s [2] 4.025 s [3] 5.4 s [4] 6.75 s

The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s2. The

distance covered by the body in the 5th second of its motion is

[1] 25 m [2] 35 m [3] 50 m [4] 85 m

A body is projected up to with a speed 'u' and the time taken by it is T to reach the maximum height H. Pick out

the correct statement

[1] It reaches H/2 in T/2 sec [2] It acquires velocity u/2 in T/2 sec

[3] Its velocity is u/2 at H/2 [4] Same speed at 2T

TIME

DIS

PLA

CE

ME

NT

F

E

D

C

A

B

t

s

O

EXERCISE # 3

)) 300600


Q.9[MP PET-95]

Q.10

[MP PET- 95]

Q.11 [AFMC-95]

Q.12

[BHU-95,CPMT-95]

Q.13

[AIIMS-96]

Q.14[RPET-96]

Q.15[RPET-1996]

Q.16

[CPMT-96]

Q.17 [AFMC-97]

Q.18

[RPET-97]

Q.19

[CPMT-97]

A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 seceach. Its initial velocity is

[1] 1 m/sec [2] 10 m/sec [3] 5 m/sec [4] 2 m/sec

A rocket is fired upward f rom the earth's surface such that it creates an acceleration of

19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface wouldbe

[1] 245 m [2] 490 m [3] 980 m [4] 735 m

A ball is thrown upwards with a velocity of 100 m/sec. It will reach the ground after

[1] 40 sec [2] 20 sec [3] 10 sec [4] 5 sec

The acceleration of a particle is increasing linearly time t as bt. The particle starts from the origin with an

initial velocity v0. The distance travelled by the particle in time t will be

[1] 3

0

1v t bt

6[2]

30

1v t bt

3[3]

20

1v t bt

3[4]

20

1v t bt

2

The displacement of a body is given to be proportional to the cube of time passed. The magnitude of the acceleration

of the body, is

[1] Increasing with time [2] Decreasing with time

[3] Constant but not zero [4] Zero

A particle starts from rest and moves with uniform acceleration. Then the ratio of distance covered in nth sec. to nsec. is

[1] 2n

2n 1[2] 2

2 1n n

[3] 2n

n 1[4] 2

2n 1n

A car moves for half of its time at 80 km/h and for rest half of time at 10 km/h. Total distance covered is 60 km.What is the average speed of the car

[1] 60 km/h [2] 45 km/h [3] 120 km/h [4] 180 km/h

A body dropped from a height h with initial velocity zero, strikes the ground with velocity 3 m/s. Another body of

same mass is dropped from the height h with an initial velocity of 4 m/s. Find the final velocity with which it strikesthe ground

[1] 3 m/s [2] 4 m/s [3] 5 m/s [4] 12 m/s

If a body starts from rest and travels 1.2 m in the 8th second then what is the acceleration

[1] 0.20 m/s2 [2] 0.16 m/s2 [3] 0.08 m/s2 [4] 0.2255 m/s2

A train is moving with uniform velocity. Suddenly, a and still train is moving with same

velocity the compartment moves to a ceratin distance and comes to rest. The distance travelled by the compartment

is how much times of the distance travelles by the train in the same time

[1] one fourth [2] Half [3] Equal [4] In uncertain ratio

A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if twostones are thrown [one upwards and other downwards] with the same velocity u and they reach the earth surface

after t1 and t

2 seconds respectively, then

[1] 1 2t t t [2] 1 2t t

t2

[3] 1 2t t t [4] 2 21 2t t t

+ + + +

−−

++

= −+

= = =


Q.20 [CPET-2002,CPMT-97]

Q.21

[EAMCET-93, CPMT-97]

Q.22

[CPMT-97]

Q.23

[BHU-98]

Q.24

[BHU-98]

Q.25[CBSE-98]

Q.26

[RPET-98]

Q.27

[CPMT-98]

Q.28

[AFMC-99]

Q.29

[RPET-99]

Q.30 [RPMT-99]

Q.31 [ CPMT-99]

By which velocity a ball be projected vertically so that the distance it covers in its 6 second is twice the distanceit covers in its 6th second -(g = 10 m/s2)

[1] 58.8 m/s [2] 49 m/s [3] 65 m/s [4] 17.5 m/s

The coordinates of a moving particle at any time are given by 2x at and 2y bt . The speed of the particle at

any moment is

[1] 2t a b [2] 2 22t a b [3] 2 2t a b [4] 2 22t a b

A particle experience a constant acceleration for 20 sec after starting from rest. If it travels a distance S1 in the

first 10 sec and a distance S2 in the next sec, then

[1] 1 2S S [2] 2

1

SS

3[3]

21

SS

2[4]

21

SS

4

A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom, starting from rest at the top.

How much time does it take to cover one-fourth the distance starting from rest at the top

[1] 1 sec [2] 2 sec [3] 4 sec [4] 16 sec

A ball released from a great height falls freely towards earth. Another body is released from the same height exactlyone second later. The separation between the two bodies after two second the release of the second body is

[1] 9.8 m [2] 49 m [3] 24.5 m [4] 19.6 m

A car moving with a speed of 40 km/hr can be stopped by applying breaks after atleast 2m. If the same car ismoving with a speed of 80 km/h. What is the minimum stopping distance

[1] 8 m [2] 2 m [3] 4 m [4] 6 m

A car travels half distance with 40 km/hr and rest half distance with 60 km/hr., then the average speed of car is


A car moves along a straight line whose equation of motion is given by 2 3s 12t 3t 2t , where[s] is in metres

and [t] in seconds. The velocity of the car at start will be

[1] 7 m/s [2] 9 m/s [3] 12 m/s [4] 16 m/s

A stone is thrown with an initial speed of 4.9 m/s from a bridge in vertically upward direction. It falls down in water

after 2 sec. The height of the bridge is

[1] 4.9 m [2] 9.8 m [3] 19.8 m [4] 24.7 m

Two car A and B are initially at rest. Now car A starts moving with a constant velocity of 40 m/s and car B starts

moving with constant acceleration of 4 m/s2. How much time will have lapsed from before the cars again meet

[1] 15 second [2] 20 second [3] 30 second [4] 35 second

A wheel covers a distance of 9.5 km in 2000 revolutions. The diameter of the wheel is

[1] 15 cm [2] 7.5 cm [3] 1.5 m [4] 7.5 m

Two trains, each 50 m long are travelling in opposite with velocity of 15 m/s. The time of crossing is

[1] 2 s [2] 10

s3

[3] 2 3 s [4] 4 3 s

= =

[ ]+ − + ( )+

= = = =

= + −


Q.32

[CPMT-99]

Q.33

[CPMT-99]

Q.34 [MPPET-2001]

Q. 35

[Karnataka-2001]

Q. 36

[Karnataka-2002]

Q. 37

[AFMC-2001]

Q.38

[UP-CPMT-2001]

Q.39 [BHU-2000]

Q.40

[Manipal-2000]

Q.41

[Manipal-2000]

Q.42[Manipal-2000]

Q.43 [AIIMS2000]

Q.44 [AIIMS-2000]

The displacement of a particle is given by 2 4y a bt ct dt . The initial velocity and acceleration are respectively

[1] b,–4d [2] –b, 2c [3] b, 2c [4] 2c, –4d

A stone is allowed to fall from from the top of a tower and covers half the height of the tower in the last second of

its journey. The time taken by the stone to reach the foot of the tower is

[1] 2 2 s [2] 2 2 s [3] 4s [4] 2 2 s

A man throws a ball vertically upward and it rises through 20 m and returns to his hands. What was the initialvelocity (u) of the ball and for how much time (T) it remained in the air (g = 10 m/s2)

[1] u = 10 m/s, T = 2s [2] u = 10 m/s, T = 4s [3] u = 20 m/s, T = 2s [4] u = 20 m/s, T = 4s

A balloon starts rising from the ground with an acceleration of 1.25 m/s2. After 8s, a stone is released from the

balloon. The stone will ( taking g = 10 ms-2)

[1] Have a displacement of 50 m [2] Cover a distance of 40 m in reaching the ground

[3] Reach the ground in 4s [4] Begin to move down after being released

A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is

thrown when the previous one is at the maximum height. If the maximum height is 5m, the number of balls thrownper minute is (take g = 10 ms-2)

[1] 120 [2] 80 [3] 60 [4] 40

Initially a body is at rest. If its acceleration is 5 m/s2, then calculate the distance travelled in the 18th sec

[1] 86.5 m [2] 87.5 m [3] 88 m [4] 89 m

A particle is moving with velocity 5 m/s towards east and its velocity changes to 5 m/s north in 10 sec. Find the

acceleration.

[1] 2 N W [2] 1

N W2

[3] 1

N E2

[4] 2 N E

A stone is dropped from a running bus. It will travel towards the ground in a

[1] straight line [2] circular path [3] parabolic path [4] none of these

A force of 1000 N is applied on a body of mass 100 kg a velocity of 5 m/s. How much time does it

require to acquire a velocity of 25 m/s

[1] 2 sec [2] 4 sec [3] 6 sec [4] 8 sec

If a freely falling body travels in the last second, a distance equal to the distance travelled by it in the first three

seconds, the time of its travel is

[1] 3 sec [2] 4 sec [3] 5 sec [4] 6 sec

A packet is dropped from a balloon which is going upward with a velocity 12 m/sec. The velocity of the packet after2 seconds will be

[1] –7.6 m/sec [2] 7.6 m/sec [3] 12 m/sec [4] –12 m/sec

If a ball is thrown vertically upwards at 40 m/s, its velocity after two seconds will be

[1] 10 m/s [2] 20 m/s [3] 30 m/s [4] 40 m/s

Velocity-time curve for a body projected vertically upwards is

[1] Ellipse [2] Parabola [3] Hyperbola [4] Straight line

= + + −

( )− ( )+ ( )±

− − − −


Q.45[AFMC-2000]

Q.46

[AFMC-2000]

Q.47[AFMC-2000]

Q.48

[RPET-2000]

Q.49

[RPMT-2000]

Q.50[RPMT-2000]

Q.51

[CPMT-2000]

Q. 52

[IIT-2000]

Q.53

[RPET-2001]

Q.54

[RPET-2001]

Q.55

[RPET-2001]

A motorcycle is moving with a velocity 80 km/hr ahead a car moving with a velocity of 65 km/hr in the samedirection. What is the relative velocity of the motorcycle with respect to the car


A body starts from rest and has an acceleration 20 cm/sec2. What is the distance covered by the body in

first 8 sec

[1] 160 cm [2] 640 cm [3] 1280 cm [4] 1640 cm

The speed of a boat is 5 km/hr in still water. If it crosses a river of width 1 km along the shortest possible path in15 minutes, then velocity of the river is


A particle travels 10 m in first 5 sec and 10 m in next 3 sec. Assuming constant acceleration what is the distance

travelled in next 2 sec

[1] 8.3 m [2] 9.3 m [3] 10.3 m [4] None of these

The displacement [s] of a body is directly proportional to the square of the time [t] than the acceleration of

the body is

[1] increases [2] constant [3] decreases [4] zero

A train covers 50 metre distance and stops when applied the breaks. If the velocity of train is just doubled andapplied the same retarding force then the distance covered by the train is

[1] 50 m [2] 100 m [3] 150 m [4] 200 m

Equation of position [x] with time [t] is given by equation x = 3t3 + 7t2 + 5t + 8. The acceleration at time t = 1s. is

[1] 18 m/s2 [2] 32 m/s2 [3] Zero [4] 14 m/s2

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 resistance, its velocity v varies with the height h above theground as

[1] h

v

d[2] h

v

d [3] h

v

d [4] h

v

d

A particle moves according to above velocity time graph. Then what is the ratio between distance travelled in last

2 seconds and 7 second

[1] 14

[2] 12

[3] 18

[4] 16

For a freely falling body ratio of distances travelled in first, second and third second of its motion will be

[1] 5 : 3 : 1 [2] 1 : 4 : 9 [3] 1 : 3 : 5 [4] 9 : 4 : 1

50 m long trains are crossing each other in opposite direction with velocity of 10 m/s and 15 m/s respectively. Then

time-taken by trains to cross each other will be

[1] 2 sec [2] 4 sec [3] 6 sec [4] 8 sec

1 3 5 7 sec

10

m/sec


Q.56[RPMT-2001]

Q.57[CPMT-2001]

Q.58 [RPET-2002]

Q.59

[CPMT-2002]

Q.60

[CPET-2003]

Q.61

[CPET-2003]

Q.62

[CPMT-2003]

Q.63

[CPMT-2003]

Q.64

[AIEEE-2004]

Q.65

[AIEEE-2004]

Q.66[AIEEE-2005]

A particle moves in east with velocity of 15 m/s for 2 sec. then moves nor thward with 5 m/s for8 sec, then average velocity of the particle is

[1] 1 m/s [2] 5 m/s [3] 7 m/s [4] 10 m/s

A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then maximum height attained byit (g = 10 m/s2)

[1] 8 m [2] 20 m [3] 10 m [4] 16 m

A body starts from rest with acceleration a = 2[t – 1] then its velocity after 5 seconds will be

[1] 15 m/s [2] 25 m/s [3] 35 m/s [4] 45 m/s

A point P consider at contact point of a wheel on ground which rolls on ground without sliping then value of

displacement of point P when wheel completes half of rotation - [If radius of wheel is 1 m]

[1] 2 m [2] 2 4 m [3] m [4] 2 2 m

A car, moving with a speed of 50 km/hr. can be stopped by brakes after at least 6 m. If the same car is moving at

a speed of 100 km/hr, the minimum stopping distance is

[1] 24 m [2] 6 m [3] 12 m [4] 18 m

The coordinates of a moving particle at any time 't' are given by 3x t amd 3y t . The speed of the particle

at time 't' is given by

[1] 2 2 2t [2] 2 2 [3] 2 23t [4] 2 2 23t

A man throws balls w ith the same speed vertically upwa ds one after the other at an interval of2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (g = 9.8

m/s2)

[1] only with speed 19.6 m/s [2] more than 19.6 m/s

[3] at least 9.8 m/s [4] any speed less than 19.6 m/s

If a ball is thrown vertically upwards with sped u, the distance covered during the last t seconds of its ascent is

[1] ut [2] 21

gt2

[3] 21

ut gt2

[4] u gt t

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any

displacement x is proportional to

[1] logex [2] ex [3] x [4] x2

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the

position of the ball at 3

T second

[1] 18

h17 meter from the ground [2]

9

h7meter from the ground

[3] 9

h8meter from the ground [4]

9

hmeter from the ground

The relation between time t and distance x is t = ax2 + bx where a and b are constants. The accelerationis -

[1] –2av3 [2] 2av2 [3] –2abv2 [4] 2bv3

p p p

a b

+ +

= =

α + β α + β α + β α + β

− [ ]+


Q.67

[AIEEE-2005]

Q.68[AIEEE-2005]

Q.69[AIEEE-2005]

Q.70

[AIEEE-2005]

Q.71

[CPMT-2005]

Q.72[CPMT-2005]

Q.73 [IIT Scr.-2005]

A car, starting from rest, accelerates at the rate f through a distance S then continues at constant speed for

time t and then decelerates at the rate 2

f to come to rest. If the total distance traversed is 15 S, then -

[1] S = 2

1ft2 [2] S =

4

1ft2 [3] S = 2ft2 [4] S =

6

1ft2

A particle is moving eastwards with a velocity of 5 ms–1 . In 10 seconds the velocity changes to 5 ms–1 northwards.The average acceleration in this time is

[1] zero [2] 2ms

2

1 towards north-west

[3] 2ms

2

1towards north-east [4]

2ms2

1 towards-north

A bullet fired into a fixed target loses half of its velocity after penentarting 3 cm. How much further it will penetratebefore coming to rest assuming that if faces constant istance to motion -

[1] 1.5 cm [2] 1.0 cm [3] 3.0 cm [4] 2.0 cm

A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2m/s2. He

reaches the ground with a speed of 3m/s. At what height, did he bail out -

[1] 293 m [2] 111 m [3] 91 m [4] 182 m

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a directionperpendicular to AB with velocity v

1. The boy at A starts running simultaneously with velocity v and catches

the other boy in a time t, where t is -

[1] 21

2 vv/a [2] )vv(/a 1 [3] )vv/(a 21

22 [4] a/(v – v1)

A ball is thrown vertically upward. It has a speed of when it has reached one half of its maximumheight. How high does the ball rise? Take g = 10 m/s2 -

[1] 20 m [2] 15 m [3] 5 m [4] 10 m

What will be the a vs x graph for the following graph?

[1] [2] [3] [4]

−

− −

+ + −


Q.74

[AIEEE-2006]

Q.75[CPMT-2006]

Q.76[CPMT-2006]

Q.77[CPMT-2006]

ANSWER KEY EXERCISE # 3Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ans.Qus. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Ans.Qus. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45Ans.Qus. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60Ans.Qus. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75Ans.Qus. 76 77Ans.

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as

v = a x . The displacement of the particle varies with time as -

[1] t [2] t1/2 [3] t3 [4] t2

A car runs at a constant speed on a crcular track of radius 100m, taking 62.8 seconds for every circular lap.the average velocity and average speed for each circular lap respectively -

[1] 0, 10 m/s [2] 10 m/s, 10 m/s [3] 10 m/s, 0 [4] 0, 0

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from Ois given by x = 40 + 12t – t3. How long would the particle travel before coming to rest.

[1] 40m [2] 56m [3] 16m [4] 24m

Two bodies, A(of mass 1kg) and B (of mass 3kg), are dropped from heights of 16m and 25m, respectively.The ratio of the time taken by them to reach the ground is

[1] 12/5 [2] 5/12 [3] 4/5 [4] 5/4

4 3 3 3 1 3 1 4 1 4 2 1 1 2 2

3 2 2 3 4 4 2 2 3 1 2 3 2 2 3

2 3 2 4 3 3 2 2 2 1 3 1 2 4 1

2 2 1 2 4 2 1 1 3 2 2 3 1 2 1

4 2 2 4 3 1 3 2 2 1 3 4 3 4 1

3 3

Kinematics Physics Problems

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