Stopping, thinking and braking distances

In a nutshell

The thinking distance of a vehicle is how far the vehicle travels during the driver's reaction time. The braking distance is the distance taken for the vehicle to stop once the driver applies the brakes. The stopping distance is the sum of thinking and braking distance.

Stopping distance

The stopping distance is the overall distance over which a vehicle travels, from the moment the driver perceives a hazard, until the moment the car comes to rest. The formula to calculate stopping distance is shown below:

$stopping \space distance = thinking \space distance \space + braking \space distance$

In an emergency, a driver may perform an emergency stop. During an emergency stop, the maximum force is applied by the brakes, so that the vehicle stops in the shortest possible distance.

The longer it takes to perform an emergency stop, the higher the risk of a collision. So, the shorter a vehicle's stopping distance, the safer it is.

In general, the heavier a vehicle is, or the faster it's travelling, the longer it's stopping distance will be.

Thinking distance

The thinking distance is how far the vehicle travels during the driver's reaction time. The reaction time is defined as the time between the driver seeing the hazard and applying the brakes of the vehicle.

A driver's thinking distance is predominantly affected by two things:

Factor	Explanation
Driver's speed	The faster the driver is going, the greater the distance the vehicle will cover for the same reaction time.
Driver's reaction time	The longer the driver's reaction time, the longer their thinking distance.

A driver's reaction time can be affected by tiredness, drugs or alcohol. Distractions, such as listening to music or eating while driving, can also affect a driver's ability to react.

You can measure the reaction time of a person by either using a computer-based test, or with a ruler drop test.

Note: Resolution is defined as the smallest change that a device can detect. A computer will have a much higher resolution than a ruler when measuring reaction time.

Curiosity: Everyone's reaction time is different. A human reaction time is typically between $0.2 - 0.9\ seconds.$ 

Braking distance

The braking distance is the distance taken for the vehicle to stop once the driver applies the brakes. The braking distance is affected by the following factors:

Factor	explanation
Vehicle speed	For a given braking force, the faster the vehicle travels, the longer it takes to stop.
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.
Tyre condition	Tyres that are bald (they have no tread left) cannot expel 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.

Physics; Motion and forces; KS4 Year 10; Stopping, thinking and braking distances

Physics; Motion and forces; KS4 Year 10; Stopping, thinking and braking distances

Physics; Motion and forces; KS4 Year 10; Stopping, thinking and braking distances

Braking

When the driver presses on the brake pedal, the brake pad pushes on the rotating wheel. The brake pads do work on the wheel via friction. Energy is transferred from the kinetic energy stores of the vehicle, to the thermal energy stores of the brakes. The brakes therefore increase in temperature when braking.

To stop a vehicle, the brakes must do work to transfer all the of the energy from the vehicle's kinetic store. The formula below summarises this principle:

$\space kinetic \space energy = work \space done$

In general, the faster a vehicle is moving, the more energy it has in its kinetic energy store. This means more work is needed to be done by the brakes to stop the vehicle.

Note: One important point to note is that a vehicle's speed affects braking distance more than thinking distance. This is because the braking distance is related to the kinetic energy stores of the vehicle, and thus the work done by the brakes. If the speed of the vehicle is doubled, the kinetic energy of the vehicle will increase four-fold, along with the required work done by the brakes to stop the vehicle.