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 ?

What is meant by free fall ? Two bodies, one of mass $1\,g$ and other of mass $1\, kg$ are dropped from the same height in vacuum. Compare the two time intervals in which the two bodies will hit the ground.

A moving body is covering a distance directly proportional to the square of time. The acceleration of the body is

A car starts from rest and moves along the $x-$ axis with constant acceleration $5\, ms^{-2}$ for $8\,\sec $. If it then continues with constant velocity, what distance will the car cover in $12\,\sec $ since it started from the rest ?

A racing car has an acceleration of $4\, m s ^{-2} .$ What distance will it cover in $20$ seconds after start ?