Stopping Distances — Thinking and Braking

This lesson covers stopping distances as required by AQA GCSE Combined Science Trilogy (8464), section 6.5.3. Stopping distance questions appear frequently in AQA exams and often carry 4–6 marks, so understanding the factors that affect thinking and braking distances is essential.

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What Is Stopping Distance?

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

Term	Definition
Thinking distance	The distance the vehicle travels during the driver's reaction time (between seeing a hazard and pressing the brake)
Braking distance	The distance the vehicle travels after the brakes are applied until it comes to a complete stop
Stopping distance	The total distance from when the driver sees the hazard to when the vehicle stops

graph LR
    H["Hazard seen"] -->|"Thinking distance"| B["Brakes applied"]
    B -->|"Braking distance"| S["Vehicle stops"]
    H -.->|"Stopping distance = thinking + braking"| S

    style H fill:#e74c3c,color:#fff
    style B fill:#f39c12,color:#fff
    style S fill:#27ae60,color:#fff

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Thinking Distance

Thinking distance depends on:

• The speed of the vehicle — higher speed means a greater distance covered during reaction time.
• The driver's reaction time — a longer reaction time means a greater thinking distance.

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

Factors That Increase Reaction Time

Factor	Why it increases reaction time
Tiredness / fatigue	Slower brain processing
Alcohol	Impairs judgement and slows reflexes
Drugs (legal or illegal)	Many drugs slow reaction time
Distractions (phone, passengers, radio)	Delays the driver noticing the hazard
Age	Reaction times tend to increase with age
Illness	Can slow mental processing

Exam Tip (AQA 8464): Factors affecting thinking distance are all about the driver. They affect how quickly the driver reacts. Speed also affects thinking distance because $d = s \times t$d=s×t.

Worked Example

A driver has a reaction time of 0.7 s and is travelling at 20 m/s. Calculate the thinking distance.

Solution:

$\text{Thinking distance} = 20 \times 0.7 = 14$Thinking distance=20×0.7=14 m

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Braking Distance

Braking distance depends on:

• The speed of the vehicle — higher speed means more kinetic energy to dissipate.
• The condition of the road — wet, icy or oily roads reduce friction.
• The condition of the brakes — worn brake pads reduce braking force.
• The condition of the tyres — worn tyres with low tread depth reduce grip.
• The mass of the vehicle — heavier vehicles have more kinetic energy.

Factors That Increase Braking Distance

Factor	Why it increases braking distance
Wet / icy / oily roads	Reduced friction between tyres and road
Worn brakes	Brakes apply less force
Worn tyres (low tread)	Less grip on the road surface
Higher speed	More kinetic energy to transfer
Greater vehicle mass	More kinetic energy to transfer

Exam Tip: Factors affecting braking distance are about the vehicle and the road conditions. They are NOT about the driver.

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How Speed Affects Stopping Distance

As speed increases:

• Thinking distance increases linearly (proportional to speed — double the speed, double the thinking distance).
• Braking distance increases with the square of speed (double the speed, quadruple the braking distance).

This is because kinetic energy = $\frac{1}{2}mv^2$21​mv2. Doubling speed quadruples the kinetic energy, which must all be converted to thermal energy in the brakes.

Speed (mph)	Speed (m/s)	Thinking distance (m)	Braking distance (m)	Stopping distance (m)
20	9	6	6	12
30	13	9	14	23
40	18	12	24	36
50	22	15	38	53
60	27	18	55	73
70	31	21	75	96

flowchart TD
    S["Increasing Speed"]
    S --> TD["Thinking distance increases LINEARLY"]
    S --> BD["Braking distance increases with SPEED SQUARED"]
    TD --> SD["Stopping distance = Thinking + Braking"]
    BD --> SD

    style S fill:#e74c3c,color:#fff
    style TD fill:#f39c12,color:#fff
    style BD fill:#c0392b,color:#fff
    style SD fill:#27ae60,color:#fff

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Braking Force and Energy Transfer

When the brakes are applied:

• The braking force does work on the vehicle to decelerate it.
• The vehicle's kinetic energy is transferred to thermal energy in the brakes (the brakes get hot).
• $W = F \times s$W=F×s (work done = braking force × braking distance).

Worked Example

A car of mass 1200 kg is travelling at 20 m/s. Calculate the braking force needed to stop it in 40 m.

Solution:

Step 1: Calculate kinetic energy. $KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 1200 \times 20^2 = \frac{1}{2} \times 1200 \times 400 = 240\,000$KE=21​mv2=21​×1200×202=21​×1200×400=240000 J

Step 2: Use $W = F \times s$W=F×s (work done = kinetic energy transferred). $240\,000 = F \times 40$240000=F×40 $F = \frac{240\,000}{40} = 6000$F=40240000​=6000 N

The braking force is 6000 N.

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Dangers of Large Decelerations

Very large decelerations (emergency braking, crashes) are dangerous because:

• The forces on passengers and the vehicle are very large ($F = ma$F=ma, large $a$a means large $F$F).
• Brakes may overheat, reducing braking effectiveness (brake fade).
• Tyres may lose grip and the vehicle may skid — the driver loses control.
• On wet or icy roads, large braking forces are more likely to cause skidding.

Exam Tip (AQA 8464): When discussing large decelerations, link to $F = ma$F=ma: a large deceleration requires a large force, which can cause injury to passengers and damage to the vehicle.

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Reaction Time Measurement

Typical human reaction time is approximately 0.2 s to 0.9 s.

Methods to measure reaction time:

1. Ruler drop test — measure how far a ruler falls before it is caught.
2. Computer-based test — click a button when a stimulus appears.

The ruler drop test uses the equation $s = \frac{1}{2}gt^2$s=21​gt2 to convert the distance the ruler falls into a reaction time.

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