$A$ bus is moving with a velocity $10 \, m/s$ 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 velocity should the scooterist chase the bus? (in $m/s$)

Two particles $A$ and $B$ are moving along a straight line with $B$ ahead of $A$. If their velocities remain constant,what will be the effect on the magnitude of their relative velocity when $A$ is ahead of $B$?

$A$ 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 $d$ 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 $A$ and $B$ are travelling in the same direction with velocities $V_A$ and $V_B$ $(V_A > V_B)$. When the car $A$ is at a distance $S$ behind the car $B$,the driver of the car $A$ applies the brakes producing a uniform retardation $a$. There will be no collision when:

$A$ ball is dropped from a building of height $45 \, m$. Simultaneously,another ball is thrown up with a speed of $40 \, ms^{-1}$. Calculate the relative speed of the balls as a function of time.