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

(a) 2a/3b

(b) a/b

(c) a/3b

(d) 0


Given x = at2-bt3

Velocity V = dx/dt

= 2at-3bt2

Acceleration = dV/dt

= 2a-6bt

Acceleration = 0

=> 2a-6bt = 0

=> 6bt = 2a

=> t = 2a/6b

= a/3b

Hence option c is the answer.

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