Stopping Distance

Stopping happens in two phases. First the driver has to notice and react; the car carries on at full speed. Then the brakes turn kinetic energy into heat.

Reaction distance

It grows in a straight line with speed. At 100 km/h (27.8 m/s) every second of hesitation costs 28 metres.

Braking distance

The tires can push back with a force of at most $\mu m g$, where $\mu$ is the friction coefficient between rubber and road. Setting the work done by that force equal to the car's kinetic energy $\tfrac{1}{2} m v^{2}$, the mass cancels:

Here $\theta = \arctan(\text{grade})$ is the slope angle, positive uphill. On level ground the bracket is simply $\mu$.

• Braking distance goes with the square of speed: double the speed, four times the distance.
• It is inversely proportional to grip: a wet road ($\mu \approx 0.5$) needs 60 % more room than a dry one ($\mu \approx 0.8$).
• Vehicle mass does not appear. A heavier car needs more force but has more load on its tires to generate it.