$A$ bus is moving with a velocity $10\, ms^{-1}$ 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? ......... $ms^{-1}$

$A$ man is $45 \, m$ behind the bus when the bus starts accelerating from rest with an acceleration of $2.5 \, m/s^2$. With what minimum velocity should the man start running to catch the bus?

Two cars $A$ and $B$ are moving in the same direction with velocities $30 \, m/s$ and $20 \, m/s$. When car $A$ is at a distance $d$ behind car $B$,the driver of car $A$ applies brakes,producing a uniform retardation of $2 \, m/s^2$. There will be no collision when ......... $m$.

$A$ 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?

$A$ 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 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 $B$?