Account for the following:
$(a)$ Name the quantity which is measured by the area occupied below the velocity$-$time graph.
$(b)$ Give an example of an object moving in a certain direction with acceleration in the perpendicular direction.
$(c)$ Under what condition is the magnitude of average velocity of an object equal to its average speed?
$(d)$ Give 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 a revolution?

(N/A) The area under a velocity$-$time graph represents the displacement (or distance if the motion is in a straight line).
$(b)$ An example is the motion of a satellite in a circular orbit or uniform circular motion,where the acceleration is directed towards the center (centripetal acceleration) while the velocity is tangential.
$(c)$ The magnitude of average velocity is equal to the average speed when the object moves in a straight line without changing its direction.
$(d)$ The motion of a freely falling body under gravity is an example of uniformly accelerated motion.
$(e)$ For a circular path of radius $r$,after half a revolution,the distance covered is half the circumference,which is $\pi r$. The displacement is the shortest distance between the initial and final points,which is the diameter of the circle,$2r$.