In the equation for acceleration (with known $v$, $u$ and $s$) why velocity is squared and displacement is multiplied by 2?

Question

In the following equation $$a = \frac{v^2 − u^2 } {2s} ,$$ where $v$ is the final velocity, $u$ is the initial velocity, and $s$ is displacement. Why is velocity squared and displacement multiplied by 2?

Answer 1

The kinematic equation for constant acceleration $$a = \dfrac{(v^2 − u^2 )} {2s}$$ can be changed to the following equation where $m$ is the mass of the object and $F$ is the force acting on the object.

$$\frac 12 m v^2 - \frac 12 m u^2 = ma\, s = F\, s$$

The left hand side is the change in the kinetic energy of the object and the right hand side is the work done on the object by an external force.