$A$ particle moves along a straight line such that its displacement at any time $t$ is given by $s = t^3 - 6t^2 + 3t + 4$ meters. The velocity when the acceleration is zero is ........ $m s^{-1}$.

$A$ car moving along a straight highway with a speed of $126 \; km/h$ is brought to a stop within a distance of $200 \; m$. How long (in $seconds$) does it take for the car to stop?

The relation between time $t$ and displacement $x$ is $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. If $v$ is the velocity,the retardation is:

The velocity of a bullet is reduced from $200\; m/s$ to $100\; m/s$ while travelling through a wooden block of thickness $10\; cm$. The retardation,assuming it to be uniform,will be ........... $\times 10^4\; m/s^2$.

If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20 \ m/s$ to a value approaching zero at $s=30 \ m$,then the acceleration of the particle at $s=15 \ m$ is $........$

If a body loses half of its velocity on penetrating $3 \, cm$ in a wooden block,then how much will it penetrate more before coming to rest? (in $cm$)