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The position x of a particle varies with...

The position `x` of a particle varies with time `t` as `x=at^(2)-bt^(3)`. The acceleration at time `t` of the particle will be equal to zero, where (t) is equal to .`

A

`(2a)/(3b) `

B

`b/a`

C

`a/(3b)`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
C
Given `x = at^(2) -bt^(3)`
Velocity , `v = (dx) /(dt) = (at^(2) -bt^(3)) =2at - 3bt^(2)`
Acceleration , `a = (dv)/(dt) = (d) / (dt) (2at = 3bt^(2)) = 2a - 6bt`
when a = 0 then 0 = 2a - 6bt or t `= a / (3b)`
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