$A$ $120\, m$ 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 $, s$)

$A$ bus is moving with a speed of $10\; m/s$ 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 speed should the scooterist chase the bus? (in $m/s$)

Explain the concept of relative displacement and its various cases.

Two particles start simultaneously from the same point and move along two straight lines,one with uniform velocity $v$ and the other with a uniform acceleration $a$. If $\alpha$ is the angle between the lines of motion of the two particles,then the least value of relative velocity will be at time given by

$A$ particle is dropped from rest and another particle is thrown downward simultaneously with initial speed $u$. Then:

$A$ 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: