$A$ 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 $\,s$)?

$A$ 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?

$A$ $120\, m$ long train $A$ is moving with a speed of $20\, m/s$. $A$ train $B$ of length $130\, m$ is moving with a speed of $30\, m/s$ in the opposite direction. Calculate the time taken by the trains to cross each other. (in $, s$)

$A$ $210 \ m$ long train is moving due North at a speed of $25 \ m/s$. $A$ small bird is flying due South a little above the train with a speed of $5 \ m/s$. The time taken by the bird to cross the train is $........ \ s$.

$A$ ball is dropped from the top of a building of height $80 \,m$. At the same instant,another ball is thrown upwards with a speed of $50 \,m/s$ from the bottom of the building. The time at which the balls will meet is ........ $s$.

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: