Under what condition will the magnitude of the displacement be equal to the distance travelled by an object?

$(a)$ 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.

$(a)$ Define acceleration.
$(b)$ $A$ stone describes a circular path with a constant speed. State the type of motion of the stone.

Account for the following:
$(a)$ What is the shape of the path of a body when it is in uniform motion?
$(b)$ Give one example of non-uniform motion.
$(c)$ Two cars $A$ and $B$ have their $x-t$ graph as shown in the figure. Which has greater velocity?
$(d)$ What is the quantity which is measured by the area occupied below the velocity-time graph?
$(e)$ $A$ body is moving with a velocity of $10 \, m/s$. If the motion is uniform,what will be the velocity after $10 \, s$?

$(i)$ What can be depicted from the graph regarding the motion of the object?
$(ii)$ Find the value of acceleration from the graph.

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.