Two cars $A$ and $B$ are travelling in the same direction with velocities $v_1$ and $v_2$ $(v_1 > v_2)$. When car $A$ is at a distance $d$ ahead of car $B$,the driver of car $A$ applies the brake,producing a uniform retardation $a$. There will be no collision when:

Train $A$ is moving along two parallel rail tracks towards north with speed $72 \ km/h$ and train $B$ is moving towards south with speed $108 \ km/h$. The velocity of train $B$ with respect to $A$ and the velocity of the ground with respect to $B$ are (in $ms^{-1}$):

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 at a distance $d$ behind a bus. The bus starts from rest and moves away from the man with a constant acceleration $a$. At the same time,the man starts running towards the bus with a constant velocity $v$. Which of the following statements are correct?

Two trains along the same straight rails are moving with constant speeds of $60\, km/hr$ and $30\, km/hr$ respectively towards each other. If at time $t = 0$,the distance between them is $90\, km$,the time when they collide is ......... $hr$.

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