Stopping Distance

This lesson covers stopping distance, thinking distance, braking distance, and the factors that affect each — as required by the Edexcel GCSE Physics specification (1PH0), Topic 1: Key Concepts of Physics. You need to understand the equation linking these distances, know the factors that affect each, and understand the dangers of large decelerations.

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What Is Stopping Distance?

When a driver sees a hazard and applies the brakes, the car does not stop instantly. The total distance it takes to stop is called the stopping distance.

stopping distance = thinking distance + braking distance

Thinking Distance

Thinking distance is the distance the vehicle travels during the driver's reaction time — the time between seeing the hazard and pressing the brake pedal.

During the thinking distance, the vehicle continues at the same speed because no braking force has yet been applied.

thinking distance = speed × reaction time

Braking Distance

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

During the braking distance, the braking force decelerates the vehicle.

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Reaction Time

A driver's reaction time is the time between seeing a stimulus (hazard) and responding to it (pressing the brake). A typical reaction time is 0.2 to 0.9 seconds.

Factors That Increase Reaction Time

Factor	How It Affects Reaction Time
Tiredness (fatigue)	Slows the brain's processing speed
Alcohol	Impairs brain function and slows nerve responses
Drugs (legal or illegal)	Can slow brain function and reaction speed
Distractions	Using a phone, talking to passengers, adjusting controls — delays noticing the hazard
Age	Older drivers generally have slightly slower reaction times
Illness	Can reduce alertness and slow responses

Exam Tip: Any factor that increases reaction time will increase thinking distance, which increases the overall stopping distance. The vehicle still travels at the same speed, but for a longer time, so it covers more distance before braking begins.

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Measuring Reaction Time — The Ruler Drop Test

You can measure reaction time using a simple experiment:

1. One person holds a ruler vertically, with the zero mark at the top.
2. The test subject places their thumb and finger at the bottom of the ruler (at the 0 cm mark) without touching it.
3. The first person drops the ruler without warning.
4. The test subject catches it as quickly as possible.
5. Read the distance the ruler fell from the scale.
6. Use the equation t = √(2d/g) to calculate the reaction time, where d is the distance fallen (in metres) and g = 9.8 m/s².

Example Calculation

If the ruler falls 18 cm (0.18 m):

t = √(2 × 0.18 ÷ 9.8) = √(0.0367) = 0.19 s

To improve reliability, repeat the test several times and calculate the mean reaction time.

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Factors That Affect Thinking Distance

Since thinking distance = speed × reaction time:

1. Speed — the faster the vehicle, the greater the thinking distance.
2. Reaction time — any factor that increases reaction time (see above) increases thinking distance.

Worked Example

A car is travelling at 20 m/s. The driver has a reaction time of 0.6 s. Calculate the thinking distance.

Thinking distance = speed × reaction time = 20 × 0.6 = 12 m

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Factors That Affect Braking Distance

Factor	How It Affects Braking Distance
Speed	Higher speed → much greater braking distance (braking distance is proportional to speed²)
Road conditions	Wet, icy or oily roads reduce friction → longer braking distance
Tyre condition	Worn or under-inflated tyres reduce grip → longer braking distance
Brake condition	Worn brake pads provide less braking force → longer braking distance
Mass of vehicle	Greater mass → more kinetic energy to dissipate → longer braking distance

The Effect of Speed on Braking Distance

The relationship between speed and braking distance is not linear — it follows a square law. If the speed doubles, the braking distance quadruples.

This is because the kinetic energy (KE = ½mv²) that must be converted to thermal energy by the brakes is proportional to v².

Speed	Relative Braking Distance
v	d
2v	4d
3v	9d

Worked Example

At 20 m/s, a car has a braking distance of 14 m. Estimate the braking distance at 40 m/s.

Speed has doubled (×2), so braking distance quadruples (×4): Braking distance = 14 × 4 = 56 m

Exam Tip: The relationship between speed and braking distance is proportional to speed squared. If the speed triples, the braking distance increases by a factor of 9. This is a very common calculation in the exam.

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Stopping Distance — Full Worked Example

A car is travelling at 30 m/s. The driver's reaction time is 0.5 s. The braking distance at this speed is 75 m. Calculate the stopping distance.

Step 1: Thinking distance = speed × reaction time = 30 × 0.5 = 15 m Step 2: Stopping distance = thinking distance + braking distance = 15 + 75 = 90 m

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Braking Force and Deceleration

When brakes are applied, a braking force acts on the wheels. This force does work to transfer kinetic energy to thermal energy in the brakes (the brakes get hot).

Using F = ma:

• A larger braking force produces a larger deceleration.
• A larger mass requires a larger braking force for the same deceleration.

The Danger of Large Decelerations

Large decelerations are dangerous because:

1. They require very large braking forces, which can cause the brakes to overheat and fail.
2. Large forces on passengers can cause serious injury or death.
3. At very high decelerations, the tyres may lose grip and the vehicle may skid.

If the braking force is too large:

• The wheels may lock (stop rotating), causing the vehicle to skid on the road surface.
• Skidding increases braking distance because sliding friction is less than rolling friction.
• This is why anti-lock braking systems (ABS) are used — they prevent the wheels from locking.

Exam Tip: If asked about the dangers of large decelerations, focus on the forces involved: large decelerations require large forces (F = ma), which can injure passengers, overheat brakes, and cause skidding. Always link your answer back to the physics.

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Summary