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Question

A body moves in a circle of radius 1 m, whose speed varies with time t(in s) as v=2t2 ms1. Find the net acceleration at t=2 seconds.
  1. 1616 m/s2
  2. 3240 m/s2
  3. 3814 m/s2
  4. 4160 m/s2


Solution

The correct option is D 4160 m/s2
Let the tangential acceleration be at
at=dvdt=4t
at|t=2=4(2)=8 m/s2

Let the centripetal acceleration be ac
ac=v2R
ac|t=2 sec=[2(2)2]21=82 m/s2=64 m/s2

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

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