The position $x$ of a particle varies with time $t$ as $x = at^2 - bt^3$. The acceleration of the particle will be zero at time $t$ equal to

If the displacement ($s$ in metre) of a moving particle in terms of time ($t$ in second) is $s = t^3 - 6t^2 + 18t + 9$,then the minimum velocity attained by the particle is (in $m \ s^{-1}$)

If $v = x^2 - 5x + 4$,find the acceleration of the particle when the velocity of the particle is zero.

The acceleration-time graph for a particle moving along the $x$-axis is shown in the figure. If the initial velocity of the particle is $-5 \, m/s$, the velocity at $t = 8 \, s$ is ....... $m/s$.

If the velocity of a particle is $(10 + 2t^2) \ m/s$,then the average acceleration of the particle between $2 \ s$ and $5 \ s$ is..........$m/s^2$.

For the acceleration-time $(a-t)$ graph shown in the figure, the change in velocity of the particle from $t=0$ to $t=6 \, s$ is ........ $m/s$.