[[$$ E_{\text{liike}} = W_{\text{kitka}} $$]]
[[$$ \frac{1}{2}mv^2 = F_{\text{kitka}}s\quad |:F_{\text{kitka}} $$]]
[[$$ \frac{1}{2F_{\text{kitka}}}mv^2=s $$]]
[[$$ s=\frac{1}{2F_{\text{kitka}}}mv^2 $$]]
How is the braking distance affected if the speed of the vehicle is doubled? Instead of the one-fold speed [[$ v $]], we will substitute the two-fold speed [[$ 2v $]].
[[$$ s=\frac{1}{2F_{\text{kitka}}}m(2v)^2=\frac{1}{2F_{\text{kitka}}}m\cdot 4v^2= 4\cdot\frac{1}{2F_{\text{kitka}}}mv^2 $$]]
Therefore the braking distance is quadrupled as speed is doubled.
