The displacement of a particle starting from rest at t = 0 is given by s = 9 t 2 - 2 t 3 . The time in…

The velocity of particle is, $v=\frac{ds}{dt}=\frac{d\left(9t^2-2t^3\right)}{dt}=18t-6t^2$

When particle attains zero velocity, $v=18t-6t^2=0$

$$\begin{gathered} 18t-6t^2=0 \\ \Rightarrow 6t\left(3-t\right)=0 \\ \Rightarrow t=0 \text{and} t=3 \end{gathered}$$

Therefore, after $3 \mathrm{s}$ the particle will attain zero velocity.