Two cars are moving in the same direction with a speed of $30 \, km/h$. They are separated from each other by $5 \, km$. $A$ third car moving in the opposite direction meets the two cars after an interval of $4 \, minutes$. The speed of the third car is .......... $km/h$.

$A$ train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains is $x$,what should be the minimum retardation of the train to avoid a collision?

$A$ man is at a distance of $6\,m$ from a bus. The bus begins to move with a constant acceleration of $3\,m s^{-2}$. In order to catch the bus,the minimum speed with which the man should run towards the bus is $.........m s^{-1}$.

$A$ police party is moving in a jeep at a constant speed $v$. They see a thief at a distance $x$ on a motorcycle which is at rest. The moment the police see the thief, the thief starts moving with a constant acceleration $a$. Which of the following relations is true if the police are able to catch the thief?

Two skaters $P$ and $Q$ are skating towards each other. Skater $P$ throws a ball towards $Q$ every $5 \,s$ such that it always leaves her hand with speed $2 \,ms^{-1}$ with respect to the ground. Consider two cases:
$(I)$ $P$ runs with speed $1 \,ms^{-1}$ towards $Q$,while $Q$ remains stationary.
$(II)$ $Q$ runs with speed $1 \,ms^{-1}$ towards $P$,while $P$ remains stationary.
Note that irrespective of the speed of $P$,the ball always leaves $P$'s hand with speed $2 \,ms^{-1}$ with respect to the ground. Ignore gravity. At what intervals will the balls be received by $Q$?

$A$ bus starts moving with an acceleration of $2\,m/s^2$. $A$ cyclist,$96\,m$ behind the bus,starts moving simultaneously towards the bus at a constant speed of $20\,m/s$. After how many seconds will the cyclist be able to overtake the bus?