Work-energy theorem: $$ \Delta x \: F = {\frac 1 2} m v^2 $$ $$ \Delta x \: F = {\frac 1 2} m \left({v_{final}^2 - v_0^2}\right)$$ $$ \Delta x \: m a = {\frac 1 2} m \left({v_{final}^2 - v_0^2}\right)$$ $$ \Delta x \: a = {\frac 1 2} \left({v_{final}^2 - v_0^2}\right)$$