5. (20 points) A car brakes to a complete stop. It is known that the speed at the midpoint of the distance was 100 km/h. Determine its initial speed.
Answer: 141.1 km/h.

Solution. Equations of motion for each half of the braking distance: $\frac{s}{2}=\frac{v_{0}^{2}-v^{2}}{2 a}$, and $\frac{s}{2}=\frac{v^{2}-0^{2}}{2 a}$. We obtain $v_{0}=\sqrt{2} v=141.4$ km/h.