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

$A$ man on a rectilinearly moving cart,facing the direction of motion,throws a ball straight up with respect to himself.

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:

The distance between two particles is decreasing at the rate of $6 \,m/s$. If these particles travel with the same speeds and in the same direction,then the separation increases at the rate of $4 \,m/s$. The speeds of the particles are:

Two cars are travelling towards each other at a speed of $20 \,m \,s^{-1}$ each. When the cars are $300 \,m$ apart, both the drivers apply brakes and the cars retard at the rate of $2 \,m \,s^{-2}$. The distance between them when they come to rest is: (in $\,m$)

Write the relation between instantaneous velocity and relative velocity for uniform motion.