v² = u² + 2as

So now we have the equations:
v = u + at
s = ½ (u+v) t
s = ut + ½ at²

All three have t in them - it would be useful to get rid of it. Starting with the first equation, we can write: t = (v-u)÷a. This can be substituted into the second:

s = ½ (u+v) t
s = ½ (u+v) (v-u)÷a

Expanding the brackets, and multiplying out the ½ and a:

2as = (u+v)(v-u)
2as = v² - u²

This rearranges to: v² = u² + 2as

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