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 ......... $m$.

Two balls are projected upward simultaneously with speeds $40 \, m/s$ and $60 \, m/s$. The relative position $(x)$ of the second ball with respect to the first ball at time $t = 5 \, s$ is .......... $m$ [Neglect air resistance].

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 ......... $s$.

$A$ 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? ......... $ms^{-1}$

Which one of the following time-displacement graphs represents two moving objects $P$ and $Q$ with zero relative velocity?

$A$ 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 $g = 10 \, m/s^2$).