$A$ particle is moving in a circular path of radius $r$. The displacement after half a circle would be:

State whether the following statement is true or false:
$A$ body is said to be at rest if it does not change its position with respect to its reference point.

Two cars moving in opposite directions cover the same distance $d$ in one hour. If the cars were moving in a north-south direction,what will be their displacement in one hour?

$(a)$ Differentiate between distance and displacement.
$(b)$ Under what conditions is the magnitude of average velocity of an object equal to its average speed?

$A$ train is travelling at a speed of $90\, km\, h^{-1}$. Brakes are applied so as to produce a uniform acceleration of $-0.5\, m\, s^{-2}$. Find how far the train will go before it is brought to rest. (in $, m$)

$(a)$ $A$ 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.