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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