Stopping Distances and Vehicle Safety
Stopping Distances and Vehicle Safety
When a driver sees a hazard and applies the brakes, the car does not stop instantly. The total distance it travels before coming to rest is the stopping distance, and understanding the factors that affect it is crucial for road safety.
Stopping Distance = Thinking Distance + Braking Distance
Thinking distance is the distance the car travels during the driver's reaction time — the time between seeing the hazard and pressing the brake pedal.
Braking distance is the distance the car travels after the brakes are applied until it comes to a complete stop.
stopping distance = thinking distance + braking distance
Thinking Distance
Thinking distance depends on:
- Speed — the faster you are going, the further you travel in the same reaction time
- Reaction time — typically 0.6 to 0.9 seconds for a healthy, alert driver
Factors that increase reaction time (and therefore thinking distance):
- Tiredness (fatigue)
- Alcohol or drugs
- Distractions (using a mobile phone, adjusting the radio, talking to passengers)
- Age or illness
Thinking distance is directly proportional to speed — if speed doubles, thinking distance doubles (because distance = speed x time, and reaction time is constant).
Example: At 30 mph (~13 m/s), with a reaction time of 0.7 s:
Thinking distance = 13 x 0.7 = 9.1 m
At 60 mph (~27 m/s):
Thinking distance = 27 x 0.7 = 18.9 m (roughly doubled)
Braking Distance
Braking distance depends on:
- Speed — at higher speeds, the car has more kinetic energy to dissipate
- Braking force — a greater force reduces braking distance
- Road conditions — wet, icy, or gravelly roads reduce friction, increasing braking distance
- Tyre condition — worn or under-inflated tyres have less grip
- Brake condition — worn brake pads apply less force
- Mass of vehicle — a heavier car has more kinetic energy at the same speed
Braking distance is not directly proportional to speed. Because kinetic energy depends on speed squared (KE = 0.5 x m x v squared), doubling the speed quadruples the braking distance.
Typical Stopping Distances
| Speed | Thinking distance | Braking distance | Total stopping distance |
|---|---|---|---|
| 20 mph | 6 m | 6 m | 12 m |
| 30 mph | 9 m | 14 m | 23 m |
| 40 mph | 12 m | 24 m | 36 m |
| 50 mph | 15 m | 38 m | 53 m |
| 60 mph | 18 m | 55 m | 73 m |
| 70 mph | 21 m | 75 m | 96 m |
Notice how braking distance grows much faster than thinking distance as speed increases.
The Physics of Braking
When brakes are applied, friction between the brake pads and the brake disc converts kinetic energy into thermal energy (heat). The brakes, discs, and tyres all heat up.
The work done by the braking force equals the kinetic energy lost:
work done = braking force x braking distance
and:
kinetic energy = 0.5 x mass x velocity squared
So: braking force x braking distance = 0.5 x m x v squared
Rearranging: braking distance = (m x v squared) / (2 x braking force)
This confirms that braking distance is proportional to v squared.
Danger of braking too hard: If the braking force is very large, the brakes can cause the wheels to lock, and the car skids. When skidding, the tyres slide over the road surface and have less friction (sliding friction is less than static friction), which actually increases stopping distance and the driver loses steering control.
Anti-lock braking systems (ABS) prevent the wheels from locking by rapidly applying and releasing the brakes. This keeps the tyres gripping the road, allowing the driver to maintain steering control during emergency braking.
Required Practical: Investigating Reaction Time
Method 1 — The ruler drop test:
1. One person holds a ruler vertically at the 0 cm mark at the top
2. The second person places their thumb and finger at the bottom of the ruler without touching it
3. The ruler is dropped without warning, and the second person catches it as quickly as possible
4. The distance the ruler falls is read from where the thumb grips
5. The further the ruler falls, the longer the reaction time
6. Repeat several times and calculate a mean, discarding any obvious anomalies
The reaction time can be calculated from the distance using:
t = square root of (2d / g)
where d is the distance fallen and g = 9.8 m/s squared.
Method 2 — Computer-based test:
A screen changes colour or shows a stimulus, and the person clicks a button as fast as possible. The computer measures the reaction time directly. This is more accurate and easier to repeat.
Exam Tips
- Always split your answer into thinking distance and braking distance — explain factors for each SEPARATELY
- Remember that thinking distance is proportional to speed, but braking distance is proportional to speed SQUARED
- In calculations, show that doubling speed quadruples kinetic energy and therefore braking distance
- For six-mark questions, include specific examples (tiredness increases reaction time, wet roads reduce friction) rather than vague statements