The motion of a particle along a straight line is described by equation : `x = 8 + 12 t - t^3` where `x` is in metre and `t` in second. The retardation of the particle when its velocity becomes zero is.

Options

A. `12ms^(-2)`
B. `24ms^(-2)`
C. zero
D. `6ms^(-2)`

Answer

a

Explanation

`x=8+12t-t^(3)`
`v=(dx)/(dt)=12-3t^(2)`
`a=(dv)/(dt)=-6t`
For v=0
`12-3t^(2)=0`
`t^(2)=4`
`t=+2,-2 rArr t=2s`
The retardation of particle at t=2 s is
`aa=-6xx2=-12m//s^(2)`