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)/(2)s`
B. `(2)/(3)s`
C. `(1)/(2) s `
D. `1 s `

Answer

A

Explanation

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