Question

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

• A. $24\, m\, s^{-2}$
• B. zero
• C. $6\, m\, s^{-2}$
• D. $12\, m\, s^{-2}$

Answer 1

Answer: (D)

Given : $x=8+12 t-t^{3}$
Velocity, $v=\frac{d x}{d t}=12-3 t^{2}$
When $v=0,12-3 t^{2}=0$
or $t=2 s$
$a=\frac{d v}{d t}=-6 t $
$\left.a\right|_{t=2\, s }=-12 \,m s ^{-2} $
Retardation $=12\, m s ^{-2}$