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Question

If a particle has velocity v(t)=186t m/s, the magnitude of average velocity in 10 sec is

A
10 m/s
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B
12 m/s
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C
10 m/s
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D
8 m/s
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Solution

The correct option is B 12 m/s
We know that the average speed is given by ¯v=Total displacementTotal time taken
Also, total displacement is given by
xfxi=t0(186t)dt=[18t3t2]t0=18t3t2 m
Let particle be at origin at t=0 xi=0
and, at t=0,xf=0
also, at t=10,xf=18×103×102=120 m
and total time taken is 10 sec
Thus, ¯v=12010=12 m/s
Hence, the magnitude of the average velocity is 12 m/s

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