The displacement of a particle starting from rest (at $t = 0$) is given by $s = 6{t^2} – {t^3}$. The time in seconds at which the particle will attain zero velocity again, is ….. $\sec$

A particle located at $x= 0$ at time $ t= 0 $, starts moving along with the positive $x-$direction with a velocity $v$ that varies as $v$ $=$ $\alpha \sqrt x $. The displacement of the particle varies with time as

The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\,[1 – {e^{ – bt}}]$. Then the velocity of the particle is

Let us cell a motion, $A$ when velocity is positive and increasing $A^{-1}$ when velocity is negative and increasing. $R$ when velocity is positive and decreasing and $R^{-1}$ when velocity is negative and decreasing. Now, match the following two columns for the given $s=t$ graph.

The velocity time graph of a body moving in a straight line is shown in figure.The ratio of displacement to distance travelled by the body in time $0$ to $10\,s$ is