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. (a) ` 24 m//s^2`
B. (b) ` zero`
C. (c ) ` 6 m//s`
D. (d) ` 12 m//s^2`

Answer

(d)

Explanation

Here, ` x = 8 + 12 t-t^3`
:. ` When velocity is zero (v=0) . The
` 12 -3 t^3 =0 ` or ` 12 =3 t^2 ` or t^2 =4` :. ` t=2 s`
Also, ` a= (dv)/(dt) = d/(dt) (12 -3 t^2) =- 6t`
At ` t= 2 s a =- 6 t =- xx 2 =- 12 m//s^2`
So retardation is ` 12 m//s^(2)`.