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Question

A particle moves in a circle of radius 4 m at a speed given by v=4t, where v is in m/s and t in seconds. The total acceleration of particle at t=1 s is :

A
4 m/s2
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B
43 m/s2
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C
8 m/s2
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D

42 m/s2
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Solution

The correct option is D
42 m/s2
Given that particle is moving in circular path of radius (r=4 m) with speed, v=4t. It means that it is a case of non-uniform circular motion.

The acceleration of particle will contain tangential acceleration at as well as centripetal acceleration, ac.




We know that acceleration is the rate of change of velocity per unit of time.

at=dvdtat=ddt(4t)=4 m/s2

at t=1s, v=4 m/s, hence centripetal acceleration,
ac=v2r ac=424=4 m/s2
Total acceleration aT of particle given by:
aT=at2+ac2 aT=42+42=42 m/s2

Hence option D is the correct answer.

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