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Question

The acceleration- time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial velocity?

A
12 s
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B
5 s
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C
8 s
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D
16 s
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Solution

The correct option is C 8 s
We know that under area under at graph represents change in velocity.
Let A1 and A2 be the areas of upper and lower triangle respectively.

Particle will acquire the initial velocity again when,
A1+A2=0|A1|=|A2|
A1=12×10×4=20
A2=12×(to4)×(x)=20
x(to4)=40(1)
Since the slope of line remains same,
104=xto4(2)
Solving (1) and (2), we get
x=10 and to=8 s
Hence particle will acquire its initial velocity at 8 s

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