Why braking distance quadruples at double speed, and a quick mental formula.
Stopping distance means reaction distance + braking distance • Reaction distance grows LINEARLY with speed (double speed means double distance) • Braking distance grows with the SQUARE of speed (double speed means four times the distance)
At 50 km/h: reaction 15 m + braking 10 m means stopping distance 25 m. At 100 km/h (double the speed): reaction 30 m + braking 40 m means 70 m. Note what doubling the speed did. The reaction half doubled, 15 to 30. The braking half quadrupled, 10 to 40. The total did neither. It went from 25 to 70, nearly three times as far.
• Wet asphalt: braking distance about 2× longer • Packed snow: about 3× longer • Ice: up to 10× longer Example: at 100 km/h on dry asphalt the braking distance is about 40 m. On ice it can be about 400 m. Reaction distance is not affected by the road surface at all. It is set by you, by how alert you are and how much you expected what just happened.
Fast formula for braking distance on dry asphalt: (speed in tens of km/h)² × 0.4 • 30 km/h → 3² × 0.4 means 3.6 m • 50 km/h → 5² × 0.4 means 10 m • 70 km/h → 7² × 0.4 means 20 m • 90 km/h → 9² × 0.4 means 32 m Once you square it, 'a bit more speed' stops feeling like a bit more.