Derive the equation $v^{2}-u^{2}=2 a S$ graphically.

A body thrown in the vertically upward direction rises upto a height $'h^{\prime}$ and comes back to the position of its start.

Calculate :

$(a)$ the total distance travelled by the body and

$(b)$ the displacement of the body. Under what condition will the magnitude of the displacement be equal to the distance travelled by an object ?

Starting from rest a scooter acquires a velocity of $36\, km h^{-1}$ in $10 \,s$ and then brakes are applied it takes $20\, s$ to stop. Calculate acceleration and distance travelled.

A truck running at $90\, km h ^{-1}$ is brought to rest over a distance of $25\, m$. Calculate the retardation and time for which brakes are applied.

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