$A$ bus is moving with a velocity $10 \, m/s$ 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? (in $m/s$)

$A$ car is standing $200\, m$ behind a bus,which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has an acceleration of $2\, m/s^2$ and the car has an acceleration of $4\, m/s^2$. The car will catch up with the bus after a time of:

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

What are the speeds of two objects if,when they move uniformly towards each other,they get $4\,m$ closer in each second and when they move uniformly in the same direction with the original speeds,they get $4.0\,m$ closer each $10\,s$?

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

$A$ person sitting in a moving train with his face towards the engine,throws a coin vertically upwards. The coin falls ahead of the person. The train: