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

Answer

D

Explanation

Given, `x=8+12t-t^(3)`
We know, `upsilon=(dx)/(dt)` and `a=(d upsilon)/(dt)`
So, `upsilon=12-3t^(2)`
and `a=-6t`
At `t = 2 s`
`upsilon = 0` and `a = - 6t`
`rArr a=-12 ms(-2)`
So, ratardation of the particle `= 12 ms^(-2)`.