﻿ The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to 6 s.What is the average speed of the particle over the intervals in (a) and (b)? from Physics Motion in Straight Line Class 11 Manipur Board

## Chapter Chosen

Motion in Straight Line

## Book Store

Currently only available for.
CBSE Gujarat Board Haryana Board

## Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12
The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to 6 s.
What is the average speed of the particle over the intervals in (a) and (b)?

a)

Distance travelled by the particle = Area under the given graph.

= (1/2) × (10 - 0) × (12 - 0)

= 60 m

b)

Let s1 and s2 be the distances covered by the particle between time = 2 s to 5 s and t = 5s to 6 s respectively.

Total distance (s) covered by the particle in time t = 2 s to 6 s is,

s = s1 + s2                     … (i)
For distance s1

Let u1 be the velocity of the particle after 2 s, and
a1 be the acceleration of the particle in t = 0 to t = 5s.

The particle undergoes uniform acceleration in the first 5 seconds.

Therefore, using first equation of motion v = u+at, we have

12 = 0 + a1 × 5

i.e.,  a1 = 12/5  = 2.4 m/s2

Again, using the first equation of motion, we have

v at

= 0 + 2.4 × 2

= 4.8 m/s

Distance travelled by the particle between time 2 s and 5 s i.e., in 3 s

s1 = u1 t + (1/2) a1 t

= 4.8 × 3 + (1/2) × 2.4 × (3)

= 25.2 m                                   ...(ii)

For distance s2

Let a2 be the acceleration of the particle between time t = 5 s and t = 10 s.

Using first equation of motion,

v = u + at

0 = 12 + a2 × 5

a2 = -12 / 5 = - 2.4 ms-2

Therefore,

Distance travelled by the particle in 1s (i.e., between = 5 s and t = 6 s),

s2u2 t + (1/2)a2 t2

= 12 × 1 + (1/2) (-2.4) × (1)

= 12 - 1.2 = 10.8 m                 ...(iii)

Now, from equations (i), (ii) and (iii), we have

s = 25.2 + 10.8 = 36 m

∴ Average speed = 36 / 4 = 9 m/s

801 Views

Can a body be always at rest in some frame?

Yes, a body is always at rest in a frame which is fixed with the body itself.
746 Views

What is the most essential thing to study the motion of a body?

The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion.
650 Views

What is rest?

When an object does not change its position with time, with respect to it's surroundings. In such a case the object is said to be at rest.
1215 Views

What is motion?

When an object changes it's position with time, with respect to it's surroundings, the object is said to be in motion.
657 Views

Is absolute rest or absolute motion possible?

Absolute rest and absolute motion is not possible because there is no point in the universe which is at rest and can be taken as point of reference. The planet Earth is in continuous motion.
1986 Views