v=u+at, so (v-u)/a=t	--(1)

also see that the average speed is (v+u)/2

distance = average speed * time

  s = (v+u)/2 * t

substitute t from equation (1)

  s= (v+u)/2 * (v-u)/a

rearranging...

2as = (v+u)(v-u) = v^2 - u^2

so v^2 = u^2 + 2as