Speed and stopping distances
In a nutshell
The stopping distance of a car is the sum of the thinking distance and braking distance. The thinking distance is distance travelled between the moment a hazard is seen, and the moment brakes are applied. The braking distance is the distance travelled between the brakes being applied and the vehicle coming to a complete stop.
Equations
DESCRIPTION | EQUATION |
Thinking distance | thinking distance=reaction time×speed |
Stopping distance | stopping distance=thinking distance+braking distance |
Thinking, braking and stopping distances
Speed (Mph) | | | | |
Speed (ms−1) | | | | |
Thinking distance (m) | | | | |
Braking distance (m) | | | | |
Stopping distance (m) | | | | |
Note: you do not need to remember these values.
Thinking distance
The thinking distance is the distance travelled during a driver's reaction time. The reaction time is defined as the time between seeing a hazard and applying the brakes.
The thinking distance is proportional to the initial speed the car is travelling at, the faster the car is travelling, the longer the stopping distance, as can be seen in the table above. It can be calculated using the equation:
thinking distance=reaction time×speed
The thinking distance is proportional to the speed the driver is travelling at, as reaction time is constant without external factors, which are shown below:
FACTOR | EXPLANATION |
Driver's speed | The faster the driver is going, the greater the distance the vehicle will cover for the same reaction time, as can be seen in the table above. |
Driver's reaction time | The longer the driver's reaction time, the longer their thinking distance. This can be affected by tiredness and being under the influence or drugs. |
Note: the average human reaction time is 0.2 s.
Braking distance
The braking distance is the distance travelled between the brakes being applied and the vehicle coming to a complete stop.
FACTOR | EXPLANATION |
Vehicle speed | The faster the driver is going, the longer it takes to stop, as seen in the table at the beginning of the summary |
Weather or road surface | If there is less grip between the vehicle's tyres and the road, it can cause the vehicle to skid, which increases the braking distance of the vehicle. Water, ice, oil or leaves on the road surface all reduce the available grip of the vehicle's tyres, making it more likely to skid. |
Tyre condition | Tyres that have no tread left cannot remove water in wet conditions effectively, which can cause the vehicle to skid. |
Brake condition | Worn brakes will not be able to apply as much braking force, meaning the vehicle will take longer to stop. |
Mass of vehicle | A more massive vehicle will have a larger braking distance as it will have more kinetic energy to dissipate in the brakes. |
To stop the vehicle, the brakes must do work to transfer all the energy from the vehicles kinetic store:
W=EkFd=21mu2d∝u2
The braking distance of the car is proportional to the initial speed of the car squared, u2, as the maximum braking force and mass of the vehicle will be constant.
Stopping distance
The stopping distance of a car is defined as the total distance from when the driver sees the hazard to when the vehicle comes to a complete stop. The stopping distance consists of the thinking distance and braking distance, as shown in the word equation:
stopping distance=thinking distance+braking distance
In general, the heavier the vehicle, the longer the stopping distance will be.
Stopping distance graphs
The following graph is a stopping distance graph, which is a form of velocity-time graph. The total stopping distance travelled can be obtained by calculating the area under the graph.
When the graph is flat, this represents the thinking distance as the driver has not applied their brakes, and therefore not slowed down. When there is a slope the driver has applied the breaks as they are now slowing down.
Example:
In the UK Highway Code, the thinking distance at 50 mph (22.2 ms−1) is shown as 15 m. Calculate the corresponding reaction time.
State variables:
speed=22.2 ms−1, thinking distance=15m
State equation:
thinking distance=reaction time×speed
Sub in and solve:
reaction time=speedthinking distancereaction time=22.215reaction time=0.68 s
The reaction time is 0.68 s.