For a train engine moving with speed of $20 \;ms ^{-1}$. the driver must apply brakes at a distance of $500 \;m$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $\sqrt{ x }\; ms ^{-1}$. The value of $x$ is $…………..$ (Assuming same retardation is produced by brakes)

A bus moving along a straight highway with speed of $72 \mathrm{~km} / \mathrm{h}$ is brought to halt within $4 \mathrm{~s}$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is__________.$\mathrm{m}$.

Two cars $A$ and $B$ at rest at same point initially. If $A$ starts with uniform velocity of $40\, m/sec$ and $B$ starts in the same direction with constant acceleration of $4\,m/{s^2}$, then $B $ will catch $A$ after how much time………$sec$

A small electric car has a maximum constant acceleration of $1\,m / s ^2$, a maximum constant deceleration of $2\,m / s ^2$ and a maximum speed of $20\,m / s$. The amount of time it would take to drive this car $1\,km$ starting from rest and finishing at rest is $………\,s$