$A.B$ & $C$ are three objects each moving with constant velocity. A's speed is $10 {\mathrm{ms}}^{-1}$ in a direction $\overrightarrow{PQ}$. The velocity of $B$ relative to $A$ is $6 {\mathrm{ms}}^{-1}$ at an angle of, ${\cos }^{-1}\left(\frac{15}{24}\right)$ to $PQ$. The velocity of $C$ relative to $B$ is $12 {\mathrm{ms}}^{-1}$ in a direction $\overrightarrow{QP}$. Then the magnitude of the velocity of $C$ is

In the diagram shown, the displacement of particle is given as a function of time. The particle $A$ is moving under constant velocity of $9 {\mathrm{ms}}^{-1}$. The positive $B$ is moving under variable acceleration. From time $t=0\mathrm{s}$ to $t=6\mathrm{s}$, the average velocity of the particle $B$ will be equal to:

Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are $300 \mathrm{m}$ apart. Given graphs show their velocities as function of time as the trains slow down. The separation between the trains when both have stopped,... is:

A $2\mathrm{m}$ wide truck is moving with a uniform speed of $8 {\mathrm{ms}}^{-1}$ along a straight horizontal road. A pedestrain starts crossing the road at an instant when the truck is $4 \mathrm{m}$ away from him. The minimum constant velocity with which he should run to avoid an accident is;