Two cars $A$ and $B$ are initially at rest at the same point. If car $A$ starts with a uniform velocity of $40\, m/s$ and car $B$ starts in the same direction with a constant acceleration of $4\, m/s^2$,then after how much time will car $B$ catch car $A$?

$A$ truck moving with a constant velocity $12 \,m/s$ crosses a car moving from rest with uniform acceleration $2 \,m/s^2$. The distance the car has to travel from the starting point to cross the truck again is (in $\,m$)

The acceleration of a particle is increasing linearly with time $t$ as $a = 6t$. The particle starts from the origin with an initial velocity $u = 10 \ m/s$. The distance travelled by the particle after $t = 2 \ s$ will be: (in $m$)

The relation between the position $x$ and time $t$ of a particle moving in one dimension is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. When the velocity of the particle becomes zero,the displacement of the particle is ........ $m$.

Two cars $P$ and $Q$ are moving on a road in the same direction. The acceleration of car $P$ increases linearly with time,whereas car $Q$ moves with a constant acceleration. Both cars cross each other at time $t = 0$ for the first time. The maximum possible number of crossings (including the crossing at $t = 0$) is . . . . . . .

$A$ body $A$ moves with a uniform acceleration $a$ and zero initial velocity. Another body $B$ starts from the same point and moves in the same direction with a constant velocity $v$. The two bodies meet after a time $t$. The value of $t$ is: