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

Two stones are thrown up simultaneously with initial speeds of $u_1$ and $u_2$ $(u_2 > u_1)$. They hit the ground after $6 \, s$ and $10 \, s$ respectively. Which graph in the figure correctly represents the time variation of $\Delta x = (x_2 - x_1)$,the relative position of the second stone with respect to the first up to $t = 10 \, s$? Assume that the stones do not rebound after hitting the ground.

$A$ police party is moving in a jeep at a constant speed $v$. They see a thief at a distance $x$ on a motorcycle which is at rest. The moment the police see the thief, the thief starts moving with a constant acceleration $a$. Which of the following relations is true if the police are able to catch the thief?

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

$A$ 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?

$A$ 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: