The physics
With a constant acceleration a, three equations link everything:
v = u + at s = ut + ½at² v² = u² + 2as
Braking is a negative a. From speed u, the stopping distance is s = u² / 2a.
Before the brakes act, the car covers the reaction distance u × tr at full speed.
The distance s grows as u². So double the speed needs four times the road.