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Question

If velocity depends on time such that v=42t. Find out distance travelled by particle from 1 to 3 s.

A
Zero
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B
2 m
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C
3 m
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D
4 m
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Solution

The correct option is B 2 m
In order to calculate net distance we need to integrate for total path length travelled during the given time interval.

From the equation, v=42t,

It is clear that at t=2 s particle stops and after that particle's velocity becomes negative, that means the particle takes U- turn.

So, the net distance d in between t=1 s to t=3 s is given by

d=2t=1vdt+t=3t=2vdt

d=21(42t)dt+32(2t4)dt

d=(4tt2)21+(t24t)32

d=4(21)(2212)+(3222)4(32)

d=1+1=2 m

Hence, option (b) is correct.

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