$A$ car is standing $200\, m$ behind a bus,which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has an acceleration of $2\, m/s^2$ and the car has an acceleration of $4\, m/s^2$. The car will catch up with the bus after a time of:

$A$ 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?

$A$ body is projected vertically upward with speed $10 \, m/s$ and another at the same time with the same speed in the downward direction from the top of a tower. The magnitude of the acceleration of the first body with respect to the second is ...... $m/s^2$ (take $g = 10 \, m/s^2$).

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 $Q$?

$A$ motor car moving at a speed of $72\, km/h$ cannot come to a stop in less than $3.0\, s$ while for a truck this time interval is $5.0\, s$. On a highway,the car is behind the truck,both moving at $72\, km/h$. The truck driver signals an emergency stop. At what minimum distance should the car be from the truck so that it does not collide with the truck? The human response time is $0.5\, s$.

$A$ bus is moving with a speed of $10\; m/s$ on a straight road. $A$ scooterist wishes to overtake the bus in $100\; s$. If the bus is at a distance of $1\; km$ from the scooterist,with what speed should the scooterist chase the bus? (in $m/s$)