$A$ man is at a distance $d$ behind a bus. The bus starts from rest and moves away from the man with a constant acceleration $a$. At the same time,the man starts running towards the bus with a constant velocity $v$. Which of the following statements are correct?

Two cars are travelling towards each other at a speed of $20 \,m \,s^{-1}$ each. When the cars are $300 \,m$ apart, both the drivers apply brakes and the cars retard at the rate of $2 \,m \,s^{-2}$. The distance between them when they come to rest is: (in $\,m$)

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 .......... $km/h$.

$A$ boy sitting on the topmost berth in the compartment of a train which is just going to stop at a railway station,drops an apple aiming at the open hand of his brother sitting vertically below his hands at a distance of about $2 \ m$. The apple will fall:

When is the relative velocity of two moving cars zero?

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 $Q$?