The three formulas, and the gap rule
Reaktionsweg = (speed ÷ 10) × 3 · Bremsweg = (speed ÷ 10)² · Gefahrbremsung = (speed ÷ 10)² ÷ 2 · Anhalteweg = thinking + braking. At 50 km/h that is 15 + 25 = 40 m, or 27.5 m with a full-force stop.
The safe following distance is half the speedometer reading, in metres — 25 m at 50 km/h, 50 m at 100 km/h. Lorries over 3.5 t and buses must keep at least 50 m outside built-up areas whenever they exceed 50 km/h.
Run the stopping-distance simulator to watch why doubling the speed quadruples the braking distance rather than doubling it.
§4 Abs. 1 & Abs. 3 StVO
§4 StVO