In which of the following cases of motion,are the distance moved and the magnitude of displacement equal?

Draw a velocity-time graph for a body which starts to move with initial velocity $u$ under a constant acceleration $a$ for time $t$. Using this graph,derive an expression for the distance covered $S$ in time $t$.

$(a)$ What is acceleration? Write its $SI$ unit.
$(b)$ Draw velocity-time graphs for an object having:
$(i)$ Uniformly accelerated velocity.
$(ii)$ Uniformly retarded velocity.

Draw the distance$-$time graph for the following situations:
$(a)$ When a body is stationary.
$(b)$ When a body is moving with a uniform speed.
$(c)$ When a body is moving with non$-$uniform speed.

$A$ motor car slows down from $72 \ km \ h^{-1}$ to $36 \ km \ h^{-1}$ over a distance of $25 \ m$. If the brakes are applied with the same force,calculate $(i)$ total time in which the car comes to rest,and $(ii)$ total distance travelled by it until it comes to rest.

$(a)$ 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.