Motion in a Straight Line Test

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Motion in a Straight Line Test - 4

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Question 1
1 / -0

The displacement y (in metres) of a body varies with time t (in seconds) as . How long does the body take to come to rest?

A
8 seconds

B
10 seconds

C
12 seconds

D
16 seconds
Question 2
1 / -0

The distance x covered by a body moving in a straight line in time t is given by:

x² = t² + 2t + 3

The acceleration of the body will vary as

A

B

C

D
Question 3
1 / -0

The acceleration of a particle starting from rest varies with time according to the relation a = kt + c, where k and c are constants of motion.

The velocity v of the particle after a time t will be

A
kt + ct

B
(1/2)kt² + ct

C
(1/2)(kt² + ct)

D
kt² + (1/2)ct
Question 4
1 / -0

The acceleration a (in ms^-2) of a body starting from rest varies with time t (in s) according to the relation:

a = 3t + 4

The velocity of the body at time t = 2 s will be

A
10 ms^-1

B
12 ms^-1

C
14 ms^-1

D
16 ms^-1
Question 5
1 / -0

for motion in a straight line

A
position to the right of the origin is taken as positive and to the left as negative.

B
position to the left of the origin is taken as positive and to the right as negative.

C
motion away from origin is positive

D
motion towards origin is positive

Solution

To describe motion along a straight line, we can choose an axis, say X-axis, so that it coincides with the path of the object. We then measure the position of the object with reference to a conveniently chosen origin, say O, Positions to the right of O are taken as positive and to the left of O, as negative.
Question 6
1 / -0

The displacement of a body from a reference point is given by:

, where x is in metres and t is in seconds.

What is the initial velocity of the body?

A
2 ms^–1

B
3 ms^–1

C
6 ms^–1

D
12 ms^–1
Question 7
1 / -0

The position of an object moving in a straight line can be specified with reference to

A
a conveniently chosen origin

B
a triangle

C
an arbitrary star

D
another straight line

Solution

To describe motion along a straight line, we can choose an axis, say X-axis, so that it coincides with the path of the object. We then measure the position of the object with reference to a conveniently chosen origin, say O, Positions to the right of O are taken as positive and to the left of O, as negative.
Question 8
1 / -0

A body moving in a straight line with constant acceleration of 10 ms^-2 covers a distance of 40 m in the 4^th second. How much distance will it cover in the 6^th second?

A
50 m

B
60 m

C
70 m

D
80 m
Question 9
1 / -0

At t = 0, an arrow is fired vertically upwards with a speed of 98 ms^-1. A second arrow is fired vertically upwards with the same speed at t = 5 s. Then,

A
the two arrows will be at the same height above the ground at t = 10 s

B
the two arrows will reach back to their starting points at t = 20 s and t = 30 s

C
the ratio of the speed of the first arrow and that of the second arrow at t = 20 s will be 2 : 1

D
the maximum height attained by either arrow will be 980 m
Question 10
1 / -0

The displacement of a body from a reference point is given by , where x is in metres and t is in seconds. This shows that the body is

A
at rest

B
accelerating

C
decelerating

D
in uniform motion
Question 11
1 / -0

A body, starting from rest and moving with a constant acceleration, covers a distance s₁ in the 4^th second and a distance s₂ in the 6^th second. The ratio s₁/s₂ is

A

B

C

D
Question 12
1 / -0

A car is moving at a certain speed. The minimum distance over which it can be stopped is x. If the speed of the car is doubled, what will be the minimum distance over which the car can be stopped during the same time?

A
4x

B
2x

C
x/2

D
x/4
Question 13
1 / -0

Displacement (x) of a particle is related to time (t) as

x = at + bt² – ct³, where a, b and c are constants of motion.

The velocity of the particle, when its acceleration is zero, is given by

A

B

C

D
Question 14
1 / -0

In Kinematics we study

A
Ways to find velocity without going into the causes of motion.

B
Ways to find jerk without going into the causes of motion.

C
Ways to describe motion without going into the causes of motion.

D
Ways to find acceleration without going into the causes of motion.

Solution

Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.
Question 15
1 / -0

A ball falling from a tower of height 'h' covers a distance h/2 in the last second of its motion. What is the height of the tower? (Take g = 10 ms^–2)

A
58 m

B
50 m

C
60 m

D
55 m
Question 16
1 / -0

A body moving in a straight line with an initial velocity of 5 ms^–1 and a constant acceleration covers a distance of 30 m in the 3^rd second. How much distance will it cover in the next 2 seconds?

A
70 m

B
80 m

C
90 m

D
100 m
Question 17
1 / -0

A car starting from rest is accelerated at a constant rate until it attains a speed v. It is then retarded at a constant rate until it comes to rest. The average speed of the car for its entire journey is

A
zero

B

C

D
Question 18
1 / -0

The driver of a train A moving at the speed of 30 ms^–1 sights another train B moving on the same track towards his train at the speed of 10 ms^–1. He immediately applies brakes and achieves a uniform retardation of 4 ms^–2. To avoid head-on collision, what must be the minimum distance between the trains?

A
100 m

B
200 m

C
300 m

D
400 m
Question 19
1 / -0

Path length is defined as.

A
distance from origin to origin.

B
the distance from origin to maximum point

C
the total length of the path traversed by an object

D
the distance from origin to minimum point

Solution

Path length is defined as the total length of the path traversed by an object.
Unlike displacement, which is the total distance an object travels from a starting point, path length is the total distance travelled, regardless of where it travelled.
Question 20
1 / -0

Path length is a

A
scalar

B
tensor

C
Derived unit

D
vector

Solution

Path length has no particular direction and it depends upon the path chosen to reach the destination where displacement of the destination is absolute no matter what path is used to get there. So it is scaler.