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Question

A point P moves in clockwise direction on a circular path as shown in figure. The movement of P is such that it sweeps a distance s=2t3+3t2+6, where s is in metres and t is in seconds. The radius of the path is 36 m. The acceleration of P when t=1 s is


A
18 m/s2
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B
4 m/s2
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C
350 m/s2
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D
340 m/s2
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Solution

The correct option is D 340 m/s2
Given, distance covered along circular path
s=2t3+3t2+6
Velocity, v=dsdt=6t2+6t

Tangential acceleration, at=dvdt=12t+6
and radial acceleration, ac=v2R=(6t2+6t)2R=36t2(t+1)2R

At t=1 s,
at=12(1)+6=18 m/s2
ac=36(1)2(2)236=4 m/s2
Resultant acceleration at P is
a=a2t+a2c=182+42=340 m/s2

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