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

Answer

B

Explanation

`x=8+12t-t^(3)`
`v=(dx)/(dt)=12-3t^(2)`
`a=(dv)/(dt)=-6t`
putting v=0
`3t^(2)=12`
t=2 sec
`therefore a= -6xx2=-12 ms^(-2)`
`therefore` retardation `=12 ms^(-2)`