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Question

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length s=t3+5, where s is in meters and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when t = 2 s is nearly


A

13 m/s2

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B

12 m/s2

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C

7.2 m/s2

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D

14 m/s2

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Solution

The correct option is D

14 m/s2


S=t3+5
Speed,v=dsdt=3t2 and rate of change of speed =dvdt=6t
tangential acceleration at t=2S,at = 6 × 2=12m/s2
At t=2s,v=3(2)2=12m/s2
centripetal acceleration,
=v2R=14420m/s2
net acceleration=a2t+a2i14m/s2

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