$A$ particle of mass $50 \, g$ moves on a straight line. The variation of speed with time is shown in the figure. Find the force acting on the particle at $t = 2, 4,$ and $6 \, s$.

The position-time $(x-t)$ graphs for two children $A$ and $B$ returning from their school $O$ to their homes $P$ and $Q$ respectively are shown in the figure. Choose the correct entries in the brackets below:
$(a)$ $(A/B)$ lives closer to the school than $(B/A)$
$(b)$ $(A/B)$ starts from the school earlier than $(B/A)$
$(c)$ $(A/B)$ walks faster than $(B/A)$
$(d)$ $A$ and $B$ reach home at the (same/different) time
$(e)$ $(A/B)$ overtakes $(B/A)$ on the road (once/twice)

The figure shows a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion,give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?

From the velocity-time graph of a particle moving in a straight line,decide which of the following is an incorrect statement.

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 .......... $\text{m}$.

$A$ particle starts from the origin at time $t = 0$ and moves along the positive $x-$ axis. The velocity-time graph is shown in the figure. What is the position of the particle at time $t = 5\,s$ (in $,m$)?