Mention some uses of velocity-time graphs.

$A$ person is running along a circular path in a park.
$(a)$ At what point does he change his direction while running?
$(b)$ If he covers half of the circular path,what will be his displacement? Draw a diagram showing it.

The area under the velocity$-$time graph gives the value of

$(a)$ $A$ car moving with uniform velocity $u$ and uniform acceleration $a$ covers a distance $S$ in time $t$. Draw its velocity-time graph and derive an expression relating all the given physical quantities.
$(b)$ $A$ boy revolves a stone tied to a string $0.7 \, m$ long. Find the distance and displacement covered by the stone in completing two revolutions from the starting point.

State whether the following statement is true or false:
$A$ quantity which can be represented completely by magnitude alone is called a vector quantity.

Name the physical quantity which corresponds to the rate of change of momentum.