Velocity of a particle moving along a straight line is given by $v = t^2 - 3t - 4 \, (m/s)$. Find the velocity at the instant when no net force is applicable on the particle.......$m/s$ (in $.25$)

$A$ particle starts from rest and moves in a straight line. It travels a distance $2L$ with uniform acceleration and then moves with a constant velocity for a further distance of $L$. Finally,it comes to rest after moving a distance of $3L$ under uniform retardation. Then the ratio of average speed to the maximum speed $\left(\frac{\bar{V}}{V_m}\right)$ of the particle is

The figure shows the displacement of a particle moving along the $X-$axis as a function of time. The force acting on the particle is zero in the region:

What does the area enclosed by the acceleration-time graph for any time interval represent?

Refer to the graph in the figure. Match the following:

What is common in the two graphs given below?