$A$ car starts from rest and moves with uniform acceleration. Describe the shapes of the $(i)$ $x-t$, $(ii)$ $v-t$, and $(iii)$ $a-t$ graphs for this motion.

$A$ car passes three points $A$, $B$ and $C$ at $3 \text{ m/s}$, $6 \text{ m/s}$ and $9 \text{ m/s}$ respectively in a straight line with uniform acceleration. If distance $AB = 60 \text{ m}$, then find the distance $BC$. (in $m$)

Give an example of a motion where $x > 0$,$v < 0$,and $a > 0$ at a particular instant.

The average velocity of a body moving with uniform acceleration travelling a distance of $3.06 \ m$ is $0.34 \ ms^{-1}$. If the change in velocity of the body is $0.18 \ ms^{-1}$ during this time,its uniform acceleration is ......... $ms^{-2}$.

For a body moving with uniform acceleration along a straight line, the variation of its velocity $(v)$ with position $(x)$ is best represented by:

For a train engine moving with a speed of $20 \; m/s$,the driver must apply brakes at a distance of $500 \; m$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance,the train engine would cross the station with a speed of $\sqrt{x} \; m/s$. The value of $x$ is $..............$ (Assuming the same retardation is produced by the brakes).