Two stones are thrown up simultaneously with initial speeds of $u_1$ and $u_2$ $(u_2 > u_1)$. They hit the ground after $6 \, s$ and $10 \, s$ respectively. Which graph in the figure correctly represents the time variation of $\Delta x = (x_2 - x_1)$,the relative position of the second stone with respect to the first up to $t = 10 \, s$? Assume that the stones do not rebound after hitting the ground.

Two trains,one of length $100 \, m$ and another of length $125 \, m$,are moving in mutually opposite directions along parallel lines. They meet each other,each with a speed of $10 \, m/s$. If their accelerations are $0.3 \, m/s^2$ and $0.2 \, m/s^2$ respectively,then the time they take to pass each other will be ......... $s$.

$A$ $100\,m$ long train crosses a man travelling at $5\,km/h$ in the opposite direction in $7.2\,s$. The velocity of the train is $..........\,km/h$.

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 $Q$?

$A$ car travelling at $15 \,m/s$ overtakes another car travelling at $10 \,m/s$. Assuming each car is $4 \,m$ long, what is the time taken during the overtake (in $\,s$)?

Explain the concept of relative displacement and its various cases.