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

We have ,

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

When the particle is momentarily at rest, we have 

$\frac{ds}{dt}=0$ and $\frac{d^{2}s}{d{t}^2}\ne 0$ 

Now, 

$\frac{ds}{dt}=0\Rightarrow t=0,t=8$

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

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