Displacement (x) of a particle is related to time (t) as $\mathrm{x}=\mathrm{at}+{\mathrm{bt}}^2-{\mathrm{ct}}^3$ where a, b and c are constants of motion. The velocity of the particle when its acceleration is zero is given by

Velocity is $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{a}+2\mathrm{bt}-3{\mathrm{ct}}^2$  …….(i)

Acceleration is $\mathrm{a}=\frac{{\mathrm{d}}^2\mathrm{x}}{{\mathrm{dt}}^2}=2\mathrm{b}-6\mathrm{ct}$

Acceleration is zero at time t given by $0=2\mathrm{b}-6\mathrm{ct}$

or $\mathrm{t}=\frac{\mathrm{b}}{3\mathrm{c}}$. Putting this value oft in Eq. (i).

We have $\mathrm{v}=\mathrm{a}+2\mathrm{b}\cdot \frac{\mathrm{b}}{3\mathrm{c}}-3\mathrm{c}\times \frac{{\mathrm{b}}^2}{9{\mathrm{c}}^2}$

                 $\mathrm{v}=\mathrm{a}+\frac{{\mathrm{b}}^2}{3\mathrm{c}}$