Question

Derive $2as=v^2-u^2$ fast and accurate or else you would be reported

Answer 1

We will use both of the equations of motion to reach the third equation of motion. This will require a bit of algebra. S = ut + 12at^2 and v = u + at ,

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Answer 2

We know,

$v=u+at$            (first equation of kinematics)

$s=ut+\frac{at^2}{2}$         (second equation of kinematics)

Now we can modify the first equation as follows.

$v=u+at$ ⇔ $t=\frac{v-u}{a}$

Now substitute in second equation of kinematics.

$s=u(\frac{v-u}{a})+\frac{1}{2}a(\frac{v-u}{a})^2$

$s=\frac{uv-u^2}{a} +\frac{1}{2} a(\frac{v^2+u^2-2uv}{a^2} )$

$s=\frac{uv-u^2}{a} +\frac{1}{2} (\frac{v^2+u^2-2uv}{a} )$