Help with Physics question, show that: $v^2 = u^2+2as$

Question

there is a particular question I am struggling with in physics, this is it;

Starting with the equations $v = u+at$ and $s=u+v*t$, show that: $v^2 = u^2+2as$!

I don't want an answer really, all I want is an explanation to how to do it so I can at least attempt it myself.

Answer 1

First of all, one of your kinematic equations is completely wrong. The correct equations should be:

$$v=u+at$$ $$s=ut + \frac 12 at^2$$

(note the correction in the second)

The key is to eliminate $t$ by substitution. From the first, you should be able to get $\displaystyle t = \frac{v-u}{a}$

Now substitute that into the second and do the algebra. Can you proceed?