Thinking & Braking Distances

Thinking Distance

Thinking distance is the distance a vehicle travels during the driver's reaction time — the time between recognising a hazard and applying the brakes.

This distance depends on how quickly the driver reacts. Reaction time can vary due to several factors:

• Tiredness – slows reaction time
• Alcohol or drugs – impair judgement and slow reactions
• Distractions – such as mobile phones or loud music
• Age – older drivers may have slower reactions
• Visibility – poor weather or darkness can delay hazard recognition

Typical reaction times range from about 0.2 seconds (very alert) up to 0.9 seconds or more (tired or distracted).

The thinking distance can be calculated using the formula:

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

For instance, if a car is travelling at 20 m/s and the driver's reaction time is 0.75 seconds, the thinking distance is:

$$\text{Thinking distance} = 20 \times 0.75 = 15 \text{ metres}$$

Braking Distance

Braking distance is the distance a vehicle travels from the moment the brakes are applied until it comes to a complete stop.

This distance depends on several factors:

• Speed: The higher the speed, the longer the braking distance. This is because kinetic energy increases with the square of speed, so more energy must be removed to stop.
• Road conditions: Wet, icy, or oily roads reduce friction between tyres and road, increasing braking distance.
• Vehicle condition: Worn brakes or tyres reduce braking efficiency, increasing distance.
• Friction and braking force: Braking works by friction between the brake pads and wheels, and between tyres and road surface. Greater friction means a shorter braking distance.

Friction is essential for braking. If friction is low (e.g., icy roads), the braking force is less effective, so the car takes longer to stop.

For example, if a car is travelling at 20 m/s on a dry road, it might take 20 metres to stop once the brakes are applied. But on a wet road, the braking distance could be much longer.

Note: Braking distance is proportional to the square of speed, which can be written as:

$$\text{Braking distance} \propto \text{speed}^2$$

Stopping Distance

Stopping distance is the total distance a vehicle travels from the moment a hazard is spotted until it comes to a complete stop. It is the sum of thinking distance and braking distance:

$$\text{Stopping distance} = \text{Thinking distance} + \text{Braking distance}$$

Stopping distance is crucial for road safety because it determines how far ahead a driver must see to stop safely.

Speed has a large effect on stopping distance because:

• Thinking distance increases linearly with speed (directly proportional).
• Braking distance increases with the square of speed.

For example, doubling the speed roughly doubles the thinking distance but quadruples the braking distance, greatly increasing the total stopping distance.

This is why speed limits exist and why driving slower in poor conditions is safer.