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

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:

$A$ body $A$ is thrown vertically upwards with such a velocity that it reaches a maximum height of $h$. Simultaneously,another body $B$ is dropped from height $h$. It strikes the ground and does not rebound. The velocity of $A$ relative to $B$ $(V_{AB})$ versus time $(t)$ graph is best represented by: (upward direction is positive)

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

Two particles $A$ and $B$ are moving along a straight line with $B$ ahead of $A$. If their velocities remain constant,what will be the effect on the magnitude of their relative velocity when $A$ is ahead of $B$?

$A$ man is $45 \, m$ behind the bus when the bus starts accelerating from rest with an acceleration of $2.5 \, m/s^2$. With what minimum velocity should the man start running to catch the bus?