Motion in Straight Line

Physics Part I

Physics

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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)Â *t*Â = 0 s to 10 s, (b)Â *t*Â = 2 s to 6 s.

What is the average speed of the particle over the intervals in (a) and (b)?

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.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (1/2)Â Ã—Â (10 - 0)Â Ã—Â (12 - 0)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 60 m

b)Â

LetÂ

Total distance (

LetÂ u

The particle undergoes uniform acceleration in the first 5 seconds.Â

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

Â Â 12 = 0 +Â

i.e., Â

Â Â Â = 0 + 2.4 Ã— 2

Â Â Â = 4.8 m/s

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

Â Â = 4.8Â Ã—Â 3 + (1/2)Â Ã—Â 2.4Â Ã—Â (3)

Â Â = 25.2 m Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(ii)Â

LetÂ

Using first equation of motion,Â

v = u + at

0 = 12 +Â

Therefore,Â

Distance travelled by the particle in 1s (i.e., betweenÂ

s

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

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

âˆ´ Average speed = 36 / 4 = 9 m/sÂ

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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.

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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.

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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.

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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.

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