If a particle moves according to the law s=6t2−t32 , then the time at which it is momentarily at rest is

We have ,

$s = 6 t^{2} - \frac{t^{3}}{2} \Rightarrow \frac{d s}{d t} = 12 t - \frac{3 t^{2}}{2}$ and $\frac{d^{2} s}{d t^{2}} = 12 - 3 t$

When the particle is momentarily at rest, we have

$\frac{d s}{d t} = 0$ and $\frac{d^{2} s}{d t^{2}} \neq 0$

Now,

$\frac{d s}{d t} = 0 \Rightarrow t = 0, t = 8$

Clearly, $\frac{d^{2} s}{d t^{2}} \neq 0$ for $t = 0, 8$ .

Thus, the particle is momentarily at rest at $t = 0, 8$ .

If a particle moves according to the law $s = 6 t^{2} - \frac{t^{3}}{2}$ , then the time at which it is momentarily at rest is