From the given $v -t$ graph (Fig.), it can be inferred that the object is

Account for the following

$(a)$ Name the quantity which is measured by the area occupied below the velocity$-$time graph.

$(b)$ An object is moving in a certain direction with acceleration in the perpendicular directions.

$(c)$ Under what condition is the magnitude of average velocity of an object equal to its average speed ?

$(d)$ An example of uniformly accelerated motion.

$(e)$ A body is moving along a circular path of radius

$(r)$. What will be the distance and displacement of the body when it completes half revolution ?

If the displacement of a body is proportional to the time elapsed, what type of motion does the body possess ?

A body is moving, with a velocity of $10 \,m s ^{-1}$. If the motion is uniform, what will be its velocity after $10 \,s$ ?

Derive following equations for a uniformly accelerated motion

$(i)$ $v=u+a t$

$(ii)$ $S=u t+1 / 2 a t^{2}$

$(iii)$ $v^{2}-u^{2}=2 a S,$ where symbols have their usual meaning.