The bus's stopping distance — the physics behind it

The stopping distance is the total distance from the moment you see a hazard until the bus comes to a stop. It consists of two parts: the reaction distance (while you manage to react) and the braking distance (while the bus slows down).

The reaction distance grows linearly with speed, but the braking distance depends on the speed squared. So: if you double the speed, the braking distance quadruples. That is the core of why small increases in speed produce large stopping distances.

With a reaction time of 1.0 s and a deceleration of 6 m/s² (dry asphalt): at 50 km/h (13.9 m/s), s_R ≈ 13.9 m and s_B ≈ 16.1 m, i.e. about 30 m. At 80 km/h (22.2 m/s), s_R ≈ 22.2 m and s_B ≈ 41.2 m, i.e. about 63 m. The braking distance alone more than doubles, because the speed only increases ~1.6 times (1.6² ≈ 2.6).

The deceleration a is directly related to the coefficient of friction µ between tyre and road: a = µ · g, where g ≈ 9.82 m/s². On dry asphalt µ is high, on ice it is low — and because the braking distance is inversely proportional to a, the braking distance more than doubles when µ is halved. A heavy bus can rarely use all the dry road grip, because the braking system and consideration for standing passengers limit the deceleration; in practice, therefore, calculate with a lower a than pure friction allows.

With a reaction time of 1.0 s and deceleration a = 6 m/s² (dry) and a = 3.5 m/s² (wet) respectively, the stopping distances below are obtained. Notice how the distance grows much faster than the speed — because the braking distance goes with the square.