The position x of a particle varies with time t as x = at² – bt³. The acceleration of the particle will be zero at time t equal to

Position x = at² - bt³

Velocity $=\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left[{\mathrm{at}}^2-{\mathrm{bt}}^3\right]$

Velocity = 2ta – 3bt²

Acceleration = $\frac{\mathrm{dv}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left[2\mathrm{ta}-3{\mathrm{bt}}^2\right]$

Acceleration = 2a – 6bt = 0
$=2\mathrm{a}=6\mathrm{bt}\Rightarrow \mathrm{t}=\frac{\mathrm{a}}{3\mathrm{b}}$