The area under a $v-t$ graph represents a physical quantity which has the unit:

Give examples to distinguish:
$(i)$ Distance and displacement.
$(ii)$ Speed and velocity.
$(iii)$ Acceleration and retardation.

An object starting from rest travels $20 \, m$ in the first $2 \, s$ and $160 \, m$ in the next $4 \, s$. What will be the velocity after $7 \, s$ from the start (in $, m/s$)?

$A$ train $100 \, m$ long is moving with a velocity of $60 \, km/h$. Find the time it takes to cross a bridge $1 \, km$ long.

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?

What is a velocity-time graph? State how it can be used to find:
$(i)$ The acceleration of a body.
$(ii)$ The displacement of the body.
$(iii)$ The distance travelled in a given time.