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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

`alpha/beta`

B

`(2alpha)/(3beta)`

C

`alpha/(3beta)`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
C
`x=alphat^(2)-betat^(3)`
`v=(dx)/(dt)=2alphat-3betat^(2)`
`a=(dv)/(dt)=2alpha-6betat`
`a=0=2alpha-6betatimpliest=alpha/(3beta)`
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