P17: Stopping Distances
Braking distance, thinking distance and stopping distance
📋 Key Definitions
Stopping distance: The total distance a vehicle travels from the moment the driver sees a hazard to the moment the vehicle stops. Stopping distance = thinking distance + braking distance.
Thinking distance: The distance the vehicle travels during the driver's reaction time (the time between seeing the hazard and pressing the brake).
Braking distance: The distance the vehicle travels while the brakes are applied, from pressing the brake to coming to a complete stop.
Reaction time: The time between seeing a hazard and responding (pressing the brake). Typical reaction time is about 0.5 seconds.
🧠 Thinking Distance
Thinking distance depends on the driver's reaction time and the vehicle's speed.
| Factor | Effect on thinking distance | Why |
|---|---|---|
| Higher speed | Increases | Vehicle travels further during the same reaction time |
| Tiredness | Increases | Slower reactions → longer reaction time |
| Alcohol / drugs | Increases | Slows reaction time |
| Distractions (phone, music) | Increases | Delays the response to the hazard |
Thinking distance = speed × reaction time
Worked Example 1: Calculating thinking distance
A car is travelling at 20 m/s. The driver's reaction time is 0.6 s. Calculate the thinking distance.
Thinking distance = speed × reaction time = 20 × 0.6 = 12 m
🛞 Braking Distance
Braking distance depends on the vehicle's speed and factors affecting the brakes and road.
| Factor | Effect on braking distance | Why |
|---|---|---|
| Higher speed | Increases greatly | More kinetic energy to remove; braking distance increases with speed² |
| Greater mass | Increases | More kinetic energy (KE = ½mv²) |
| Wet / icy roads | Increases | Less friction between tyres and road |
| Worn tyres | Increases | Less grip on the road surface |
| Worn brakes | Increases | Reduced braking force |
📐 Effect of Speed on Stopping Distance
Both thinking distance and braking distance increase with speed, but braking distance increases much more dramatically. If speed doubles, thinking distance doubles, but braking distance increases by a factor of 4 (it is proportional to speed²).
| Speed (mph) | Thinking distance (m) | Braking distance (m) | Stopping distance (m) |
|---|---|---|---|
| 20 | 6 | 6 | 12 |
| 30 | 9 | 14 | 23 |
| 40 | 12 | 24 | 36 |
| 50 | 15 | 38 | 53 |
| 60 | 18 | 55 | 73 |
| 70 | 21 | 75 | 96 |
Why braking distance increases with the square of speed: The kinetic energy of the vehicle is KE = ½mv². If speed doubles, KE quadruples. The brakes must remove all this energy, so the braking distance is proportional to v².
⚡ Kinetic Energy and Braking
KE = ½mv²
KE = kinetic energy (J), m = mass (kg), v = speed (m/s)
When brakes are applied, the work done by the braking force must equal the kinetic energy of the vehicle:
Work done by brakes = F × d = ½mv²
F = braking force (N), d = braking distance (m)
So braking distance d = ½mv² / F
Worked Example 2: Braking distance and KE
A car of mass 1000 kg is travelling at 20 m/s. The braking force is 8000 N. Calculate the braking distance.
KE = ½mv² = ½ × 1000 × 20² = 200 000 J
F × d = KE, so d = KE / F = 200 000 / 8000 = 25 m
Worked Example 3: Effect of doubling speed
If a car's speed doubles from 10 m/s to 20 m/s, explain why the braking distance increases by a factor of 4.
At 10 m/s: KE = ½ × m × 10² = 50m
At 20 m/s: KE = ½ × m × 20² = 200m
KE has increased by 200m / 50m = 4 times. Since braking distance is proportional to KE (same braking force), the braking distance also increases by a factor of 4.
Worked Example 4: Total stopping distance
A car travels at 25 m/s. The driver's reaction time is 0.5 s and the braking distance is 35 m. Calculate the total stopping distance.
Thinking distance = 25 × 0.5 = 12.5 m
Stopping distance = 12.5 + 35 = 47.5 m
❓ Practice Questions
Q1: Foundation Define stopping distance and state the equation that links its two components.
Q2: Foundation Give two factors that increase thinking distance and two factors that increase braking distance.
Q3: Higher A car of mass 1200 kg travels at 15 m/s. The braking force is 6000 N. Calculate the braking distance.
Q4: Higher Explain, using kinetic energy, why doubling the speed of a vehicle increases the braking distance by a factor of four.
Q5: Foundation A driver is using a mobile phone. Explain how this affects their stopping distance.
✅ Answers
- Stopping distance is the total distance travelled from seeing a hazard to stopping. Stopping distance = thinking distance + braking distance.
- Thinking distance: higher speed, tiredness, alcohol/drugs, distractions. Braking distance: higher speed, wet/icy roads, worn tyres, worn brakes, greater mass.
- KE = ½ × 1200 × 15² = 135 000 J. Braking distance = KE / F = 135 000 / 6000 = 22.5 m
- KE = ½mv². If speed doubles from v to 2v, the new KE = ½m(2v)² = ½m × 4v² = 4 × ½mv². The kinetic energy is 4 times greater, so the brakes must do 4 times more work, and the braking distance increases by a factor of 4 (assuming the same braking force).
- Using a mobile phone is a distraction, which increases the driver's reaction time. This means the thinking distance increases, so the total stopping distance increases. The car travels further before the brakes are applied, increasing the risk of a collision.
🎯 Exam Tips
- Stopping distance = thinking distance + braking distance — don't multiply them
- Thinking distance is proportional to speed. Braking distance is proportional to speed²
- When asked to explain why speed affects braking distance, always use KE = ½mv² and the work done equation
- Alcohol and drugs affect thinking distance (via reaction time), NOT braking distance
- Wet/icy roads affect braking distance (via friction), NOT thinking distance
- Exam questions often ask you to estimate stopping distances — learn the typical values at 30 mph (23 m) and 70 mph (96 m)
🔬 Required Practical
Required Practical: Investigating Reaction Time
Aim: To measure human reaction time and investigate factors that affect it.
Method: 1. One person holds a ruler vertically, with the 0 cm mark at the bottom, between the thumb and forefinger of the second person. 2. The first person drops the ruler without warning. 3. The second person catches it as quickly as possible and records the distance the ruler fell (the measurement on the ruler where it was caught). 4. Repeat 3 times and calculate a mean distance. 5. Use the equation h = ½gt² (rearranged to t = √(2h/g)) to calculate the reaction time from the fall distance. 6. Repeat the test with a distraction (e.g. music, conversation) or after exercise to investigate how these factors affect reaction time.
Variables: IV: condition of the person (e.g. distracted, after exercise, after caffeine), DV: reaction time (calculated from fall distance), Control: same person, same hand, same ruler, same dropping technique, same environment.
🔢 Maths Skills
Mathematical Skills
Stopping distance = thinking distance + braking distance. Thinking distance = speed × reaction time. Braking distance relates to KE: F × d = ½mv², so d = ½mv²/F. If speed doubles, KE quadruples, so braking distance quadruples (d ∝ v²). You may also use t = √(2h/g) to calculate reaction time from ruler drop distance.
Maths Example
A car at 30 m/s has reaction time 0.7 s. Thinking distance = 30 × 0.7 = 21 m. Braking distance at 30 m/s (mass 1000 kg, braking force 7500 N): d = ½mv²/F = ½ × 1000 × 900 / 7500 = 60 m. Total stopping distance = 21 + 60 = 81 m. If speed doubles to 60 m/s: thinking distance doubles (42 m) but braking distance quadruples (240 m).
⚠️ Common Misconceptions
Watch Out!
1. Wrong: If speed doubles, the stopping distance doubles. Correct: If speed doubles, thinking distance doubles BUT braking distance increases by a factor of 4 (it is proportional to speed²). So the total stopping distance more than doubles.
2. Wrong: Worn tyres and wet roads increase the thinking distance. Correct: Worn tyres and wet roads increase the BRAKING distance (less friction). They do not affect thinking distance — that depends on reaction time and speed only.
3. Wrong: Alcohol and drugs increase braking distance. Correct: Alcohol and drugs increase THINKING distance (by increasing reaction time). They do not directly affect braking distance — the brakes work the same regardless of the driver's state.
✍️ 6-Mark Question
Extended Answer
6 marks: A car is travelling at 40 mph on a dry road. The driver has consumed alcohol. Explain how each of the following affects the total stopping distance: (i) the speed of the car, (ii) the alcohol consumed, (iii) wet road conditions.
(i) Speed affects both thinking distance and braking distance. Higher speed means the car travels further during the driver's reaction time, increasing thinking distance. More importantly, kinetic energy is proportional to speed squared (KE = ½mv²), so if speed increases, the brakes must do much more work to stop the car, and braking distance increases in proportion to speed². (ii) Alcohol slows the driver's reaction time, meaning there is a longer delay between seeing the hazard and pressing the brake. This increases the thinking distance because the car travels further before the brakes are applied. Alcohol does not affect braking distance directly. (iii) Wet roads reduce the friction between the tyres and the road surface, so the maximum braking force is reduced. With less braking force available, the braking distance increases. The car skids more easily, taking longer to stop. Wet roads do not affect thinking distance.
Mark scheme: 1 mark for speed increases thinking distance (travels further in reaction time); 1 mark for speed increases braking distance (KE ∝ v²); 1 mark for alcohol increases reaction time → increases thinking distance; 1 mark for alcohol does NOT affect braking distance; 1 mark for wet roads reduce friction → increase braking distance; 1 mark for wet roads do NOT affect thinking distance. (6 marks total)
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
The Highway Code gives the following typical stopping distances at different speeds:
| Speed (mph) | Thinking distance (m) | Braking distance (m) | Total (m) |
|---|---|---|---|
| 20 | 6 | 6 | 12 |
| 30 | 9 | 14 | 23 |
| 40 | 12 | 24 | 36 |
| 50 | 15 | 38 | 53 |
| 60 | 18 | 55 | 73 |
| 70 | 21 | 75 | 96 |
(a) Show that thinking distance is proportional to speed and calculate the reaction time assumed in the data (1 mph ≈ 0.447 m/s).
(b) Explain why the braking distance increases more rapidly than the thinking distance as speed increases.
(c) A driver on a wet road at 30 mph needs to stop for a child 25 m ahead. Use the data to evaluate whether they will stop in time, justifying your answer.
Answers: (a) At each speed, thinking distance / speed = 6/20 = 9/30 = 12/40 = 15/50 = 18/60 = 21/70 = 0.3 m per mph. This constant ratio shows proportionality. Reaction time = 0.3 m/mph ÷ 0.447 m/s per mph ≈ 0.67 s. (b) Thinking distance ∝ speed (linear), but braking distance ∝ speed² (quadratic). KE = ½mv², so doubling speed quadruples KE and therefore quadruples the work the brakes must do. (c) At 30 mph on a dry road, total stopping distance = 23 m, so the car would just stop in time. On a wet road, braking distance is roughly doubled (≈ 28 m), giving a total of about 9 + 28 = 37 m. The car would NOT stop in time — it would hit the child. The driver should have been driving more slowly in wet conditions.
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