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

Answer 1

Answer: (D)

Given : $x$ = 8 + 12 12t - t³
$\text{Velocity,} \text{v} = \frac{ d x}{ d ⁡ t} = 1 2 - 3 t^{2}$
When v = 0, 12 - 3t² = 0 or t = 2 s
$a = \frac{ d v ⁡}{ d ⁡ t} = - 6 t$
a|_{t = 2 s} = - 12 m s^-2
Retardation = 12 m s^-2