Question

Derive the following equation for a uniformly accelerated motion where the symbols have their usual meanings:

$v^2=u^2+2as$

Answer 1

From the first equation of motion,
$v=u+at$
$t=\frac{v-u}{a}...........\left(i\right)$

For a uniformly accelerated motion, $\text{Average velocity}=\frac{v+u}{2}...........\left(ii\right)$

$\text{Displacement}=\text{Average Velocity}\times \text{Time}$

Substituting from (i) and (ii),

$s=\left(\frac{v+u}{2}\right)\times \left(\frac{v-u}{a}\right)$
$\therefore v^2=u^2+2as$