The velocity $(v)$ - distance $(x)$ graph is shown in the figure. Which graph represents the acceleration $(a)$ versus distance $(x)$ variation of this system?

Fill in the blanks:
$(a)$ The path length is always ............ .
$(b)$ The slope of the velocity-time graph for an object moving with acceleration is ............ .
$(c)$ If the velocity-time graph is parallel to the time-axis,the object is ............ .

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)

$A$ rigid ball rolls without slipping on a surface shown below: Which one of the following is the most likely representation of the distance travelled by the ball versus time graph?

Draw the $v-t$ graph for constant velocity and explain it.

The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in $4 \; s$ is ......... $m$.