Stopping Distances and Braking

The stopping distance of a vehicle is the total distance travelled from the moment a driver spots a hazard to the moment the vehicle comes to rest. It is made of two parts:

$\text{stopping distance}=\text{thinking distance}+\text{braking distance}$

• Thinking distance is how far the vehicle travels during the driver's reaction time, before the brakes are touched. The car is still moving at full speed here.
• Braking distance is how far it travels once the brakes are applied, while the vehicle is slowing down.

You must be able to define stopping distance as the sum of thinking distance and braking distance, and describe the factors affecting each.

For a given braking force, the stopping distance increases as the speed increases. Both parts grow with speed, but they grow in different ways, which the next slides unpick.

Thinking distance depends on two things: the speed of the vehicle and the driver's reaction time. During the reaction time no braking has happened, so the car covers ground at a steady speed. That distance is simply speed multiplied by reaction time:

$\text{thinking distance}=\text{speed}\times \text{reaction time}$

A typical reaction time is between 0.2 s and 0.9 s. Because thinking distance is speed times a fixed reaction time, it is directly proportional to speed: double the speed and the thinking distance doubles.

Worked example — a car travels at 20 m/s. The driver has a reaction time of 0.7 s. Find the thinking distance.

$\text{thinking distance}=20\times 0.7=14\text{ m}$

The car travels 14 m before the brakes are even applied. This uses $s=vt$ (distance = speed × time).

$s=vt$ is a recall-and-apply equation. You must recall and apply it; it is not given on the equation sheet.

Anything that increases the driver's reaction time increases the thinking distance, because the car covers more ground before braking begins. The speed of the vehicle also matters directly.

Factor	Effect on thinking distance	Why
Higher speed	Increases	Car covers more distance in the same reaction time
Tiredness	Increases	Slower reactions, longer reaction time
Alcohol	Increases	Slows the brain's response
Drugs (including some medicines)	Increases	Can slow reactions or cause drowsiness
Distractions (phone, radio, passengers)	Increases	Attention is elsewhere, reaction time lengthens

Reaction time can be measured in the lab. A common method is the ruler drop test: one person holds a ruler vertically, the other catches it as it falls, and the distance the ruler falls before being caught is converted into a reaction time. A longer drop distance means a slower reaction.

Tiredness, alcohol, drugs and distractions affect the thinking distance (via reaction time), not the braking distance. Keep the two lists separate in the exam.

Once the brakes are applied, friction between the brake pads and the wheels (and between the tyres and the road) provides the force that slows the car. Braking distance is how far the car travels while this is happening.

Braking distance is increased by anything that reduces the friction available, or that increases the energy the brakes must remove:

Factor	Effect on braking distance	Reason
Higher speed	Increases sharply	More kinetic energy to remove
Wet or icy road	Increases	Less grip, so less friction between tyres and road
Worn or badly inflated tyres	Increases	Reduced grip on the road
Worn brakes	Increases	Brakes provide a smaller braking force
Larger vehicle mass (heavy load)	Increases	More kinetic energy to remove

Adverse road and weather conditions (wet, icy, leaves) and poor vehicle condition (worn brakes or tyres) increase the braking distance, not the thinking distance.

Braking is an energy transfer. When the brakes are applied, the work done by friction reduces the kinetic energy of the vehicle and raises the temperature of the brakes. The kinetic energy of the moving car is transferred to thermal energy in the brakes, pads and surrounding air.

The work done by the braking force equals the kinetic energy removed:

$W=Fs{E}_k=\frac{1}{2}m{v}^2$

Because kinetic energy depends on the square of the speed, doubling the speed gives four times the kinetic energy. To remove four times the energy over the same braking force, you need roughly four times the braking distance. This is why braking distance rises so steeply with speed while thinking distance only rises in proportion.

(Separate Physics only) You should be able to estimate how the stopping distance for a vehicle varies with different speeds and interpret speed–stopping-distance graphs. The graph of braking distance against speed curves upward because braking distance grows with speed squared.

The steep, curved rise of braking distance against speed is the shape examiners expect on a speed–stopping-distance graph:

Thinking distance rises as a straight line (proportional to speed); braking distance curves upward (proportional to speed squared).

(Higher Tier only) This slide covers estimating the forces involved in a deceleration. Higher Tier students must be able to do this; Foundation students can skip the calculation.

For a given stopping distance, a greater speed means a greater braking force is needed, which gives a greater deceleration. Very large decelerations can make the brakes overheat or cause the driver to lose control (skidding).

You can estimate the braking force by equating the work done to the kinetic energy that must be removed. Rearranging $W=Fs$ gives $F=\frac{E_k}{s}$.

Worked example — a car of mass 1200 kg travelling at 20 m/s brakes to a stop in a braking distance of 25 m. Estimate the braking force.

Step 1 — kinetic energy to be removed:

$E_k=\frac{1}{2}m{v}^2=\frac{1}{2}\times 1200\times 20^2=\frac{1}{2}\times 1200\times 400=240,000\text{ J}$

Step 2 — the braking force does this much work over 25 m, so:

$F=\frac{W}{s}=\frac{240,000}{25}=9600\text{ N}$

An estimated braking force of about 9600 N (roughly 10 kN) is typical for an emergency stop.

$E_k=\frac{1}{2}m{v}^2$ and $W=Fs$ are both recall-and-apply equations. You must recall and apply them; neither is given on the equation sheet.

1. Mixing up which factors affect which distance

Reaction-time factors (tiredness, alcohol, drugs, distractions) change the thinking distance. Road, weather and vehicle-condition factors change the braking distance. Speed and a heavy load increase both. Sort every factor into the correct column.

2. Forgetting to add both parts

Stopping distance is thinking distance plus braking distance. Calculating only one loses marks on a total-stopping-distance question.

3. Saying braking distance doubles when speed doubles

Braking distance depends on speed squared, so doubling the speed gives roughly four times the braking distance. Only thinking distance doubles when speed doubles.

4. Wrong energy transfer for braking

The kinetic energy of the car is transferred by the work done by friction to thermal energy in the brakes, raising their temperature. It is not "lost" or "used up".

5. Confusing greater force with a shorter distance

To stop in the same distance from a higher speed, a car needs a greater braking force and so a greater deceleration. A greater braking force does not, by itself, mean a longer stopping distance.