A particle moves along a straight line such that its displacement at any time $t$ is given by $s=\le

Question

A particle moves along a straight line such that its displacement at any time $t$ is given by $s=\left(2t^{3}-12 t^{2}+10 t+5\right)$ metres. The velocity when the acceleration is zero is

Professor PC Thomas Classes · Answer

(b) : Displacement $(s)=2t^{3}-12 t^{2}+10 t+5 \mathrm{~m}$. \ Velocity $(v)=\frac{d s}{d t}=6t^{2}-24 t+10$. \ Acceleration $(a)=\frac{d v}{d t}=12t-24$. \ When $a=0$, we get $12t - 24 = 0 \implies t=2$ seconds. \ Therefore, velocity when the acceleration is zero is: \ $v = 6(2)^{2}-(24 	imes 2)+10 = 24 - 48 + 10 = -14 \mathrm{~m} / \mathrm{s}$