For a particle moving on a straight line it is observed that the distance, ' $s$ ' at a time ' $t$ ' is…
For a particle moving on a straight line it is observed that the distance, ' $s$ ' at a time ' $t$ ' is given by $S=6 t-\frac{t^3}{2}$. The maximum velocity during the motion is
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Solution
$
\begin{aligned}
\text { } V & =\frac{d S}{d t}=\frac{d}{d t}\left(6 t-\frac{t^3}{2}\right) \\
V & =6-\frac{3}{2} t^2 \Rightarrow \frac{d V}{d t}=-3 t \\
\frac{d V}{d t} & =0 \Rightarrow-3 t=0 \\
\Rightarrow t & =0 \Rightarrow \frac{d^2 V}{d t^2}=-3 < 0
\end{aligned}
$
$V$ is maximum at $t=0$
$
V=6-\frac{3}{2} \times 0=6
$