The equation of motion of a particle moving along a straight line is `s=2t^(3)-9t^(2)+12t`, where the units of `s` and `t` are centrimetre and second. The acceleration of the particle will be zero after

Options

A. `3/2s`
B. `2/3s`
C. `1/2s`
D. `1s`

Answer

A

Explanation

Given `s=2t^(3)-9t^(2)+12t`
`implies(ds)/(dt)=6t^(2)-18t+12`
and `(d^(2)s)/(dt^(2))=12t-18=` acceleration
If acceleration becomes zero, then
`0=12t-18impliest=3/2s`
Hence acceleration will be zero after `3/2s`.