The stopping distance of a vehicle is the thinking distance plus the braking distance. The thinking distance is how far the vehicle travels during the driver's reaction time. The braking distance is how far it travels under the braking force. For a given braking force, the greater the speed, the greater the stopping distance. Thinking distance rises in proportion to speed, but braking distance rises faster: doubling the speed roughly quadruples it.
Reaction times differ between people and typically range from 0.2 s to 0.9 s. Tiredness, drugs, alcohol and distractions such as a phone all increase reaction time, which increases thinking distance. One simple way to measure it is the ruler drop test. A partner holds a ruler vertically, drops it without warning and you catch it. The further it falls before you catch it, the longer your reaction time. Repeating the test and taking a mean gives a better result. At 20 m/s with a reaction time of 0.5 s, the thinking distance is s = vt = 20 × 0.5 = 10 m.
Braking distance is increased by adverse road and weather conditions, such as wet or icy roads, which reduce the friction between the tyres and the road. It is also increased by poor vehicle condition, limited to worn brakes or worn tyres. These factors make it harder to stop in an emergency, so drivers need to leave bigger gaps in poor conditions.
When the brakes are applied, the friction force between the brakes and the wheels does work, which reduces the kinetic energy of the vehicle and makes the brakes hotter. The greater the speed, the greater the braking force needed to stop in a certain distance. A greater braking force gives a greater deceleration, but a very large deceleration can make the brakes overheat or cause the driver to lose control, for example by skidding. (Higher tier) The force can be estimated with F = ma: a 1000 kg car decelerating at 6 m/s2 needs a braking force of about 6000 N.