$A$ body starting from rest at $t=0$ moves along a straight line with a constant acceleration. At $t=2 \ s$,the body reverses its direction keeping the acceleration same. The body returns to the initial position at $t=t_0$,then $t_0$ is

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 . . . . . . .

$A$ particle moves along a straight line such that its displacement at any time $t$ is given by $s = t^3 - 6t^2 + 3t + 4$ meters. The velocity when the acceleration is zero is ........ $m s^{-1}$.

$A$ particle travels $10\,m$ in the first $5\,s$ and $10\,m$ in the next $3\,s$. Assuming constant acceleration,what is the distance travelled in the next $2\,s$ (in $m$)?

When is the average velocity of an object equal to its instantaneous velocity?

The displacement of a particle moving in a straight line is given by the expression $x = A t^3 + B t^2 + C t + D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is