$A$ bus starts moving with an acceleration of $2\,m/s^2$. $A$ cyclist,$96\,m$ behind the bus,starts moving simultaneously towards the bus at a constant speed of $20\,m/s$. After how many seconds will the cyclist be able to overtake the bus?

$A$ man is at a distance of $6\,m$ from a bus. The bus begins to move with a constant acceleration of $3\,m s^{-2}$. In order to catch the bus,the minimum speed with which the man should run towards the bus is $.........m s^{-1}$.

Two cars are moving in the same direction with a speed of $30\ km/h$. They are separated from each other by $5\ km$. $A$ third car moving in the opposite direction meets the two cars after an interval of $4\ minutes$. What is the speed of the third car in $km/h$?

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.

$A$ 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?

Two particles are at rest on a straight track and they are separated from each other by $100 \ m$. They start their motion in the same direction,with the same acceleration $10 \ m/s^2$. Their relative displacement after $10 \ s$ will be