$A$ body is thrown vertically upward with velocity $u$,the greatest height $h$ to which it will rise is,

The brakes applied to a car produce an acceleration of $6 \, m s^{-2}$ in the opposite direction of motion. If the car takes $2 \, s$ to stop after the application of the brakes,calculate the distance it travels during this time. (in $, m$)

$A$ train is travelling at a speed of $90\, km\, h^{-1}$. Brakes are applied so as to produce a uniform acceleration of $-0.5\, m\, s^{-2}$. Find how far the train will go before it is brought to rest. (in $, m$)

$(a)$ 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.

Derive the following equations for a uniformly accelerated motion:
$(i)$ $v = u + at$
$(ii)$ $S = ut + \frac{1}{2}at^2$
$(iii)$ $v^2 - u^2 = 2aS$, where the symbols have their usual meanings.

Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between the $4^{th}$ and $5^{th}$ seconds.