The position x of a particle varies with time as x=at2−bt3. The acceleration of particle is zero at time T equal to

ab

2a3b

a3b

Zero

A

ab

B

2a3b

C

a3b

D

Zero

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Solution

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x=at2−bt3

⇒ Velocity =dxdt=2at−3bt2

Acceleration=d2xdt2=ddt(2at−3b2)=2a−6bt

or a=2a−6bt

Making a=0

⇒2a=6bt

⇒t=dfrac2a6b=a3b.

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