The $v-t$ graph of a rectilinear motion is shown in the adjoining figure. The distance from the starting point after $8 \text{ s}$ is .......... $\text{m}$.

The speed-time graph of a particle moving along a fixed direction is shown in the figure. The distance traversed by the particle between $t = 2\,s$ to $t = 6\,s$ is........$m$

$A$ particle starts from rest and undergoes an acceleration as shown in the figure. The velocity-time graph from the figure will have which shape?

Match Column-$I$ with Column-$II$:

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?

The velocity $(v)$ of a particle moving along the $x$-axis varies with its position $(x)$ as shown in the figure. How does the acceleration $(a)$ of the particle vary with position $(x)$?