$A$ stone is thrown vertically upward with an initial velocity of $40 \, m/s$. Taking $g = 10 \, m/s^2$,find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?

$(a)$ $A$ 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.

The following graph describes the motion of a girl going to meet her friend who stays $50 \ m$ from her house.
$(i)$ How much time does she take to reach her friend's house?
$(ii)$ What is the distance travelled by the girl during the time-interval $0$ to $12$ minutes?
$(iii)$ During which time-interval is she moving towards her house?
$(iv)$ For how many minutes was she at rest during the entire journey?
$(v)$ Calculate the speed by which she returned home.

An object is moving along a straight line with uniform acceleration. The following table gives the velocity of the object at various instants of time.

Time $(s)$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
Velocity $(m s^{-1})$	$2$	$4$	$6$	$8$	$10$	$12$	$14$

Plot the graph.
From the graph:
$(i)$ Find the velocity of the object at the end of $2.5 \ s$.
$(ii)$ Calculate the acceleration.
$(iii)$ Calculate the distance covered in the last $4 \ s$.

$(a)$ Derive graphically the equation for velocity$-$time relation.
$(b)$ Name the device used to measure distance travelled by a vehicle.
$(c)$ Can displacement of a moving object be zero? Give reason.

$A$ body can have zero average velocity but not zero average speed. Justify.