Physics

8.2 - Stopping Distances

9 min

Intro and thinking distance

Braking distance

Speed and stopping distance

note 1 of 4

Stopping distance = thinking + braking distance

The stopping distance is the total distance a car travels from the moment a driver spots a hazard to when the car comes to a complete stop:

Stopping distance = thinking distance + braking distance

Thinking distance - The distance the car travels during the driver's reaction time, between noticing the hazard and applying the brakes.
Braking distance - The distance the car travels once the brakes are applied, while slowing to a stop.

In an emergency stop, the driver applies the maximum braking force to stop in the shortest possible distance.

What increases thinking distance

Higher speed - The faster the car travels, the further it goes during the reaction time.
Longer reaction time - Increased by tiredness, alcohol, drugs and distractions.

What increases braking distance

Higher speed - A faster car travels further before the braking force brings it to a stop.
Greater mass - A heavier car takes longer to stop under the same braking force.
Worn or faulty brakes - These can't apply as much braking force.
Poor road or tyre conditions - Wet or icy roads, dirt, or worn tyres reduce friction, making skidding more likely.

Two rows of cars seen from above: a slow speed row with short thinking distance and braking distance bands labelled shorter stopping distance, and a much longer fast speed row labelled greater stopping distance.

note 2 of 4

Braking transfers energy to the brakes

When the brake pedal is pushed, the brake pads press against the wheels.
The contact causes friction, so work is done between the brakes and the wheels.
This work transfers energy from the kinetic energy store of the moving car to the thermal energy store of the brakes, causing them to heat up.

Faster cars need a greater braking force

The faster a car travels, the more kinetic energy it has, so the more work the brakes must do to stop it.
To stop within a given distance, a faster car needs a greater braking force, which results in a larger deceleration.

Risks of very large decelerations

The brakes can overheat and lose effectiveness.
The tyres can lose grip and cause the car to skid.

note 3 of 4

Braking distance and work done by the brakes

To stop a car, the work done by the braking force must equal the kinetic energy of the car:

$\frac{1}{2} m v^{2} = F \times d$

Where:

$m$ = Mass of the car, in kilograms (kg)
$v$ = Speed of the car, in metres per second (m/s)
$F$ = Braking force, in newtons (N)
$d$ = Braking distance, in metres (m)

During an emergency stop the braking force $F$ is at its maximum, so the braking distance $d$ depends directly on kinetic energy:

Doubling the mass doubles the kinetic energy, doubling the braking distance.
Speed is squared ( $v^{2}$ ), so doubling the speed quadruples the kinetic energy, increasing the braking distance four-fold.

note 4 of 4

Worked example - Total stopping distance

A car travelling at 20 m/s makes an emergency stop to avoid a hazard. The braking force is 8,000 N. Estimate the total stopping distance. Take the driver's reaction time as 0.5 s and the mass of the car as 1,200 kg.

A blue car in side view with a driver, labelled mass = 1,200 kg, reaction time = 0.5 s and braking force = 8,000 N, and an arrow ahead of it marked 20 m/s.

Step 1 - Find the thinking distance

The car travels at a constant speed during the reaction time:

$d_{thinking} = v \times t = 20 \times 0.5 = 10 m$

Step 2 - Find the braking distance

Rearrange $\frac{1}{2} m v^{2} = F \times d$ for braking distance $d$ :

$\begin{matrix} d_{braking} & = \frac{\frac{1}{2} m v^{2}}{F} \\ = \frac{\frac{1}{2} \times 1,200 \times 20^{2}}{8,000} \\ = 30 m \end{matrix}$

Step 3 - Add the two distances

Stopping distance = 10 + 30 = 40 m

Step 4 - Interpretation

Thinking distance is directly proportional to speed, but braking distance is proportional to speed squared. If the speed doubled to 40 m/s, the thinking distance would double to 20 m while the braking distance would quadruple to 120 m, giving a total stopping distance of 140 m.

key terms

TermDefinition

Stopping distanceThe total distance a vehicle travels from the moment a driver spots a hazard to when it comes to a complete stop.

Thinking distanceThe distance a vehicle travels during the driver's reaction time, before the brakes are applied.

Braking distanceThe distance a vehicle travels from when the brakes are applied until it stops.

Emergency stopA stop where the driver applies the maximum braking force to halt the vehicle in the shortest possible distance.

end of notes

Key points to remember