Stopping distances · GCSE Physics

Stopping distance

The stopping distance of a vehicle is the sum of the thinking distance and the braking distance.
Thinking distance: how far the vehicle travels during the driver's reaction time. Thinking distance = speed × reaction time.
Braking distance: how far the vehicle travels under the braking force.
For a given braking force, the greater the speed, the greater the stopping distance. Example (Highway Code): 23 m at 30 mph, 96 m at 70 mph.

Reaction times vary from person to person, typically from 0.2 s to 0.9 s.
Tiredness, drugs, alcohol and distractions (such as mobile phones) make reaction times longer, increasing the thinking distance.
Reaction time can be measured with the ruler-drop test or with a computer test.

Braking distance is increased by wet or icy roads, and by poor vehicle condition, such as worn brakes or tyres.
When the brakes are applied, work is done by the friction force between the brakes and the wheel. This reduces the kinetic energy of the vehicle and the temperature of the brakes increases.
The greater the speed, the greater the braking force needed to stop in a certain distance. Large decelerations can make the brakes overheat and the driver lose control.

Use a = Δv ÷ t or v² − u² = 2 a s to find the deceleration, then F = m a to find the braking force.
Example: a 1000 kg car stopping from 20 m/s in 4 s decelerates at 5 m/s², needing a braking force of 5000 N.

Stopping distance: Thinking distance + braking distance.
Thinking distance: The distance travelled during the driver's reaction time.
Braking distance: The distance travelled while the brakes are applied, until the vehicle stops.
Reaction time: The time between seeing a hazard and reacting to it.
Braking force: The friction force from the brakes that slows the vehicle.
Deceleration: Slowing down: negative acceleration.