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Question

A body moves in a circle of radius 1 m. Its speed is given by v=2t2. Find the net acceleration at t=2 s

A
1616 m/s2
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B
3240 m/s2
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C
3814 m/s2
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D
4160 m/s2
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Solution

The correct option is D 4160 m/s2
Let the tangential acceleration be at
and centripetal acceleration be ac

Its speed is given by v=2t2

at=dvdt=4t
at t=2 s,
at=4(2)=8 m/s2

Now for the centripetal acceleration,
ac=v2R
At t=2 s,v=2×22=8 m/s
ac=821=64 m/s2

anet=a2c+a2t=642+82=4160 m/s2

Hence option D is the correct answer.

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