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  4. A particle moves along a straight line such that its displacement at any time t is given by s = (t3-6t2+3t+4) metres. The velocity when the acceleration is zero is

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Q. 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

AIPMTAIPMT 1994Motion in a Straight Line

Solution:

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