Two cars $A$ and $B$ are moving in the same direction with velocities $30 \, m/s$ and $20 \, m/s$. When car $A$ is at a distance $d$ behind car $B$,the driver of car $A$ applies brakes,producing a uniform retardation of $2 \, m/s^2$. There will be no collision when ......... $m$.

Two bodies start moving from the same point along a straight line with velocities $v_1 = 6 \, m/s$ and $v_2 = 10 \, m/s$,simultaneously. After what time will their separation become $40 \, m$?

$A$ 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)

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

$A$ body is projected vertically upward with speed $10 \, m/s$ and another at the same time with the same speed in the downward direction from the top of a tower. The magnitude of the acceleration of the first body with respect to the second is ...... $m/s^2$ (take $g = 10 \, m/s^2$).

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 $4 \, minutes$. The speed of the third car is .......... $km/h$.