$A$ man is at a distance of $6\,m$ from a bus. The bus begins to move with a constant acceleration of $3\,m s^{-2}$. In order to catch the bus,the minimum speed with which the man should run towards the bus is $.........m s^{-1}$.

Two bodies start moving from the same point along a straight line with velocities $v_1 = 6 \, m/s$ and $v_2 = 10 \, m/s$,simultaneously. After what time will their separation become $40 \, m$?

$A$ boy sitting on the topmost berth in the compartment of a train which is just going to stop at a railway station,drops an apple aiming at the open hand of his brother sitting vertically below his hands at a distance of about $2 \ m$. The apple will fall:

Two trains $A$ and $B$ of length $400 \; m$ each are moving on two parallel tracks with a uniform speed of $72 \; km \; h^{-1}$ in the same direction,with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1 \; m \; s^{-2}$. If after $50 \; s$,the guard of $B$ just brushes past the driver of $A$,what was the original distance (in $m$) between them?

$A$ 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 $\,s$)?

$A$ stone falls from the top of a tower of height $100 \text{ m}$ and at the same time another stone is projected vertically upwards from the ground with a velocity $25 \text{ m/s}$. The two stones meet after (in $\text{ s}$)