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Question

A point P moves in counter clockwise direction on a circular path a shown in figure. The movement ofP is such that it sweeps out a length s=t2+5, where s is in metre and t in second. The radius of the path is 20m. The acceleration of P when t=2s is nearly
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A
2.1m/s2
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B
12m/s2
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C
7.2m/s2
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D
14m/s2
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Solution

The correct option is A 2.1m/s2
given, distance, s=t²+5

differentiate with respect to time,

speed =v=dsdtv=2t

at t=2sec speed ,v=2×2=4m/s

so, centripetal acceleration, =ac=v2R where R is the radius of the path and R=20m. so, ac=4220=1620=0.8m/s²

now rate of change of speed, =dvdt=2

e.g., tangential acceleration at=2m/s²


now, net acceleration=a=a2t+a2c=4+0.64

=2.154m/s²



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