What you'll learn
This guide covers everything you need to know about stopping distances for your AQA GCSE Physics exam. You'll learn how to calculate stopping distances, understand the factors that affect them, and explain why road safety depends on drivers recognising these principles. This topic appears regularly in both Foundation and Higher tier papers, often in context questions about vehicle safety.
Key terms and definitions
Stopping distance — the total distance a vehicle travels from when the driver first sees a hazard until the vehicle comes to a complete stop
Thinking distance — the distance travelled by a vehicle during the driver's reaction time (from seeing a hazard to applying the brakes)
Braking distance — the distance travelled by a vehicle from when the brakes are applied until it stops completely
Reaction time — the time interval between detecting a stimulus (seeing a hazard) and responding to it (pressing the brake pedal)
Friction — the force between two surfaces that resists motion; friction between the brakes and wheels, and between tyres and road, is essential for stopping
Kinetic energy — the energy an object possesses due to its motion, calculated using ½mv²
Deceleration — the rate at which a vehicle slows down (negative acceleration)
Braking force — the force applied by the braking system to slow down or stop a vehicle
Core concepts
The stopping distance equation
The fundamental relationship you must understand is:
Stopping distance = Thinking distance + Braking distance
This equation tells us that a vehicle travels two distinct distances when stopping:
- First phase (thinking distance): The vehicle continues at constant speed while the driver reacts
- Second phase (braking distance): The vehicle decelerates once brakes are applied
For example, a car travelling at 30 mph (approximately 13 m/s) might have:
- Thinking distance: 9 m
- Braking distance: 14 m
- Total stopping distance: 23 m
You must be able to identify which factors affect each component separately, as this is a common exam question.
Factors affecting thinking distance
Thinking distance depends on two variables:
Speed of the vehicle — the faster a vehicle travels, the further it moves during the driver's reaction time. Since thinking distance = speed × reaction time, doubling the speed doubles the thinking distance (assuming reaction time stays constant).
Reaction time of the driver — typical reaction times range from 0.2 to 0.9 seconds. Several factors increase reaction time:
- Tiredness/fatigue — slower processing of information
- Alcohol and drugs — impaired nervous system function, slower responses
- Distractions — using mobile phones, eating, conversations reduce attention
- Age and experience — though both young and elderly drivers may have slower reactions
- Illness or medication — affects concentration and response speed
The condition of the vehicle does NOT affect thinking distance because the car hasn't started braking yet. Road conditions also don't affect thinking distance for the same reason.
Factors affecting braking distance
Braking distance is influenced by:
Speed of the vehicle — this has a squared relationship with braking distance. If you double the speed, braking distance increases by a factor of four. If you triple the speed, braking distance increases by a factor of nine. This is because kinetic energy is proportional to v², and all this energy must be dissipated by the brakes.
Mass of the vehicle — heavier vehicles have more kinetic energy at the same speed (KE = ½mv²), so require more work to stop them, increasing braking distance. A fully loaded lorry takes much longer to stop than an empty one.
Condition of the brakes — worn brake pads or low brake fluid reduce the braking force, increasing stopping distance. Well-maintained brakes provide maximum friction.
Condition of the tyres — worn or under-inflated tyres reduce friction with the road surface. Insufficient tread depth (legal minimum is 1.6 mm in the UK) particularly affects wet weather performance.
Road surface conditions:
- Wet roads — water reduces friction between tyres and road
- Icy roads — dramatically reduce friction, can increase braking distance by up to 10 times
- Loose surfaces (gravel, leaves, oil) — reduce grip
- Smooth/worn road surfaces — provide less friction than rough surfaces
Gradient — braking distance increases going downhill due to gravity assisting motion, and decreases going uphill as gravity opposes motion.
The physics of braking
When brakes are applied, several energy transfers occur:
The vehicle's kinetic energy is transferred to thermal energy in the brakes through friction. This is why brakes get very hot during use. The work done by the braking force equals the kinetic energy lost by the vehicle:
Work done = Braking force × Braking distance
Since work done = change in kinetic energy:
Braking force × Braking distance = ½mv²
This equation explains why braking distance increases with the square of velocity. At twice the speed, a vehicle has four times the kinetic energy, so even with the same braking force, it must travel four times the distance to dissipate this energy.
Large decelerations can be dangerous:
- May cause the vehicle to skid (losing steering control)
- Can cause brakes to overheat and fail
- Risk of injury to passengers, especially without seatbelts
- Objects in the vehicle become projectiles
Modern vehicles have anti-lock braking systems (ABS) that prevent wheels locking during emergency braking, maintaining steering control and often reducing braking distance.
Speed limits and stopping distances
UK speed limits exist partly because of the relationship between speed and stopping distance:
At 30 mph (13 m/s):
- Thinking distance: 9 m
- Braking distance: 14 m
- Total: 23 m (about 6 car lengths)
At 50 mph (22 m/s):
- Thinking distance: 15 m
- Braking distance: 38 m
- Total: 53 m (about 13 car lengths)
At 70 mph (31 m/s):
- Thinking distance: 21 m
- Braking distance: 75 m
- Total: 96 m (about 24 car lengths)
Notice that thinking distance increases proportionally with speed, but braking distance increases much more dramatically. These values assume good conditions and typical reaction time of 0.7 seconds.
Measuring reaction time
You can estimate human reaction time using simple experiments:
Ruler drop test:
- Person A holds a ruler vertically, with the zero mark between Person B's open thumb and fingers
- Person A drops the ruler without warning
- Person B catches it as quickly as possible
- Measure the distance the ruler fell
- Use d = ½gt² (with g = 10 m/s²) to calculate reaction time
For example, if the ruler falls 20 cm (0.20 m):
- 0.20 = ½ × 10 × t²
- 0.20 = 5t²
- t² = 0.04
- t = 0.2 s
This represents a very good reaction time. Typical values are 0.2-0.9 seconds.
Computer-based tests can also measure reaction time by recording the interval between a stimulus appearing on screen and a key press response. These tend to give more accurate measurements as they eliminate measurement errors.
Worked examples
Example 1: Calculating stopping distance (Foundation/Higher)
Question: A car is travelling at 15 m/s. The driver has a reaction time of 0.6 s. The braking distance of the car is 30 m. Calculate the total stopping distance. [3 marks]
Solution:
- Thinking distance = speed × reaction time [1 mark]
- Thinking distance = 15 × 0.6 = 9 m [1 mark]
- Stopping distance = thinking distance + braking distance
- Stopping distance = 9 + 30 = 39 m [1 mark]
Example 2: Explaining factors affecting stopping distance (Foundation/Higher)
Question: Explain why a driver who has been drinking alcohol will have a longer stopping distance than a sober driver travelling at the same speed. [3 marks]
Model answer:
- Alcohol slows down reaction time / impairs the nervous system [1 mark]
- This increases the thinking distance [1 mark]
- Therefore the total stopping distance increases because stopping distance = thinking distance + braking distance [1 mark]
Note: Alcohol does not directly affect braking distance (the car's braking system works the same), only thinking distance through increased reaction time.
Example 3: Applying kinetic energy concepts (Higher only)
Question: A car of mass 1200 kg is travelling at 20 m/s. The driver applies the brakes with a constant braking force of 8000 N. Calculate the braking distance. [4 marks]
Solution:
- Kinetic energy = ½mv² [1 mark]
- KE = ½ × 1200 × 20² = ½ × 1200 × 400 = 240,000 J [1 mark]
- Work done by brakes = braking force × distance
- 240,000 = 8000 × distance [1 mark]
- Distance = 240,000 ÷ 8000 = 30 m [1 mark]
This calculation assumes all kinetic energy is transferred by the braking force (no energy losses to air resistance during braking, which is a reasonable simplification for this calculation).
Example 4: Comparing stopping distances (Foundation/Higher)
Question: A car travelling at 30 m/s has a braking distance of 90 m in dry conditions. Estimate the braking distance for the same car at 30 m/s on an icy road. Explain your answer. [3 marks]
Model answer:
- Ice reduces friction between tyres and road [1 mark]
- This reduces the braking force, so more distance is needed to remove the kinetic energy / stop the car [1 mark]
- Braking distance could increase by up to 10 times, so approximately 900 m [1 mark]
(Accept answers in the range 450-900 m with suitable explanation)
Common mistakes and how to avoid them
Confusing which factors affect thinking vs braking distance — Create a table to memorise this. Remember: driver factors affect thinking distance; vehicle and road factors affect braking distance; speed affects both.
Forgetting that braking distance increases with the square of speed — Don't assume a simple proportional relationship. At double the speed, kinetic energy is four times greater, so braking distance is approximately four times longer (not just twice).
Stating that alcohol/tiredness affects braking distance — These factors only affect the driver's reaction time, not how the brakes work. Be precise: they increase thinking distance and therefore total stopping distance.
Not including units in calculations — Always state units for distance (m or metres) and time (s or seconds). Marks are often lost for missing units on final answers.
Thinking ABS brakes reduce thinking distance — Anti-lock braking systems only affect braking distance (and vehicle control), not reaction time or thinking distance.
Using Highway Code values incorrectly — The Highway Code gives stopping distances at specific speeds in good conditions. In exams, use values given in the question rather than trying to recall memorised Highway Code figures unless specifically asked.
Exam technique for stopping distance questions
"Explain" questions require reasons — Don't just state that stopping distance increases; explain the mechanism (e.g., "increased speed means more kinetic energy, requiring more work to stop the vehicle, so braking distance increases").
Identify the command word carefully — "Calculate" requires working and a numerical answer with units. "Describe" needs observations without explanation. "Explain" requires causal reasoning linking factors.
Show your working in calculations — Even if your final answer is wrong, you can earn method marks. Write the equation, substitute values, then calculate. For a 3-mark calculation, expect: equation (1 mark), substitution (1 mark), answer with unit (1 mark).
Use data from the question — Examiners often provide speed, mass, reaction time or other values. Make sure you use all relevant data given and don't introduce different numbers from memory.
Quick revision summary
Stopping distance equals thinking distance plus braking distance. Thinking distance depends on speed and reaction time (affected by alcohol, drugs, tiredness, distractions). Braking distance depends on speed squared, vehicle mass, brake condition, tyre condition and road surface. When brakes apply, kinetic energy transfers to thermal energy through friction. Speed has the greatest effect because kinetic energy is proportional to v², so doubling speed quadruples braking distance. Understanding these relationships is essential for road safety and appears frequently in AQA GCSE exam questions.