Question

A particle moves along a straight line such that its displacement at any time $t$ is given by $s=(t^3-6t^2+3t+4)$ metres.
The velocity when the acceleration is zero is

• A. 3 m/s
• B. 42 m/s
• C. -9 m/s
• D. -15 m/s

Answer 1

Answer: (C)

Displacement $(s)=t^3-6t^2+3t+4$ metres.
velocity $(v)=\frac{ds}{dt}=3t^2-12t+3$
acceleration $(a)=\frac{dv}{dt}=6t-12$.
When $a=0$, we get $t=2$ seconds.
Therefore velocity when the acceleration is zero
(v) $=3\times (2{)}^2-(12\times 2)+3=-9m/s$.