$A$ moving body is covering a distance directly proportional to the square of time. The acceleration of the body is

The velocity$-$time graph of an ascending passenger lift is as shown in the figure below.
$(i)$ Identify the kind of motion of the lift represented by lines $OA$ and $BC$.
$(ii)$ Calculate the acceleration of the lift:
$(a)$ During the first two seconds.
$(b)$ Between the $3^{rd}$ and $10^{th}$ second.
$(c)$ During the last two seconds.

The following table shows the position of three persons between $8.00\, am$ to $8.20\, am$.

Time	Position of Person $A$ $(km)$	Position of Person $B$ $(km)$	Position of Person $C$ $(km)$
$8.00\, am$	$0$	$0$	$0$
$8.05\, am$	$4$	$5$	$10$
$8.10\, am$	$13$	$10$	$19$
$8.15\, am$	$20$	$15$	$24$
$8.20\, am$	$25$	$20$	$27$

$(i)$ Who is moving with constant speed?
$(ii)$ Who has travelled the maximum distance between $8.00\, am$ to $8.05\, am$?
$(iii)$ Calculate the average speed of person $A$ in $km\, h^{-1}$.

$(a)$ Derive the second equation of motion $S = ut + \frac{1}{2}at^2$ graphically,where the symbols have their usual meanings.
$(b)$ $A$ car accelerates uniformly from $18 \text{ km h}^{-1}$ to $36 \text{ km h}^{-1}$ in $5 \text{ s}$. Calculate the acceleration and the distance covered by the car in that time.

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 determines the direction of motion of an object: velocity or acceleration?