The $v-t$ graphs of two moving objects make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. Find the ratio of their accelerations.

The velocity-time graph for a particle moving in a straight line is shown in the figure. The average velocity between $t=4 \,s$ and $t=6 \,s$ is . . . . . . (in $\,ms^{-1}$)

The motion of an airplane is represented by a velocity-time graph as shown below. The distance covered by the airplane in the first $30.5 \ s$ is . . . . . . $km$.

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 graph of displacement $s$ versus time $t$ is given below. Its corresponding velocity-time graph will be:

$A$ 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 $6 \, s$.