Reaction Time and Braking

This lesson covers human reaction time, stopping distances and the factors that affect them — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to understand the concepts of thinking distance and braking distance, how to measure reaction time experimentally, and the dangers of large decelerations.

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Stopping Distance

When a driver sees a hazard and needs to stop, the stopping distance is the total distance the vehicle travels from the moment the driver first sees the hazard to the moment the vehicle comes to a complete stop.

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 this time, the car continues at its original speed (no braking force yet).

Thinking distance = Speed × Reaction time

Braking Distance

Braking distance is the distance the vehicle travels after the brakes are applied until the vehicle stops.

During this time, the braking force decelerates the car.

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Reaction Time

Reaction time is the time between detecting a stimulus (e.g. seeing a hazard) and responding to it (e.g. pressing the brake).

Typical Reaction Times

• A typical human reaction time is 0.2 to 0.9 seconds.
• Most people have a reaction time of about 0.6 to 0.7 seconds in normal driving conditions.

Factors That Increase Reaction Time

Factor	How It Increases Reaction Time
Tiredness / fatigue	The brain processes information more slowly when tired
Alcohol	Slows brain function and nerve signals
Drugs (legal and illegal)	Many drugs slow the nervous system and impair judgement
Distractions (e.g. mobile phone, passengers)	Attention is divided, delaying the recognition of hazards
Age	Reaction times generally increase with age
Illness	Can impair concentration and response speed

Exam Tip: The factors affecting reaction time all affect thinking distance, NOT braking distance. Thinking distance depends on the driver; braking distance depends on the vehicle and road conditions.

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Core Practical: Measuring Reaction Time (Ruler Drop Test)

This is a required practical in the Edexcel GCSE Physics specification.

Method

1. One person holds a ruler vertically at the 0 cm mark at the top, with the other person's open hand at the bottom of the ruler (at a known starting mark, e.g. 0 cm between their fingers).
2. Without warning, the first person drops the ruler.
3. The second person catches the ruler as quickly as possible by closing their fingers.
4. Read the distance the ruler has fallen from where the fingers caught it.
5. Use the equation s = ½gt² to calculate the reaction time from the distance fallen.
6. Repeat at least 5 times and calculate a mean.

Calculating Reaction Time from Distance

Rearranging s = ½gt²:

t = √(2s / g)

Where:

• s = distance fallen (m)
• g = 9.8 m/s²
• t = reaction time (s)

Worked Example 1

A student catches the ruler after it has fallen 18 cm (= 0.18 m).

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

Common Results Table

Distance Fallen (cm)	Reaction Time (s)
5	0.10
10	0.14
15	0.18
20	0.20
25	0.23
30	0.25

Improving the Experiment

• Repeat multiple times and take a mean to improve reliability.
• The catcher should not look at the dropper's hand — use a verbal signal for "ready" but not for the actual drop.
• Use the same hand each time for consistency.
• Discard any obvious outliers (e.g. if the catcher anticipated the drop).

Exam Tip: You must be able to describe this experiment in detail, including how to improve its accuracy and reliability. A common exam question asks you to explain how you would use this method to investigate the effect of a variable (e.g. caffeine) on reaction time.

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Factors Affecting Braking Distance

Factor	Effect on Braking Distance	Explanation
Higher speed	Greatly increases braking distance	More kinetic energy to dissipate; braking distance ∝ speed²
Wet or icy roads	Increases braking distance	Reduced friction between tyres and road
Worn tyres	Increases braking distance	Less grip → less friction
Worn brakes	Increases braking distance	Less braking force can be applied
Heavy vehicle	Increases braking distance	More kinetic energy (KE = ½mv²) to dissipate
Downhill slope	Increases braking distance	Component of weight acts in the direction of motion

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The Relationship Between Speed and Stopping Distance

Thinking Distance is Proportional to Speed

If speed doubles, thinking distance doubles (direct proportion).

This is because: thinking distance = speed × reaction time, and reaction time stays the same.

Braking Distance is Proportional to Speed Squared

If speed doubles, braking distance quadruples (increases by a factor of 4).

This is because the kinetic energy (KE = ½mv²) of the car is proportional to v². The brakes must do work equal to the kinetic energy to stop the car. If KE quadruples, the braking distance quadruples (assuming the braking force stays the same).

Worked Example 2

At 20 mph, a car's thinking distance is 6 m and braking distance is 6 m.

At 40 mph (double the speed):

• Thinking distance = 6 × 2 = 12 m (proportional to speed)
• Braking distance = 6 × 2² = 6 × 4 = 24 m (proportional to speed²)
• Stopping distance = 12 + 24 = 36 m

At 60 mph (triple the speed):

• Thinking distance = 6 × 3 = 18 m
• Braking distance = 6 × 3² = 6 × 9 = 54 m
• Stopping distance = 18 + 54 = 72 m

Typical Stopping Distances

Speed	Thinking Distance	Braking Distance	Stopping Distance
20 mph (32 km/h)	6 m	6 m	12 m
30 mph (48 km/h)	9 m	14 m	23 m
40 mph (64 km/h)	12 m	24 m	36 m
50 mph (80 km/h)	15 m	38 m	53 m
60 mph (97 km/h)	18 m	55 m	73 m
70 mph (113 km/h)	21 m	75 m	96 m

Exam Tip: The key mathematical relationship to remember is: if speed doubles, thinking distance doubles but braking distance quadruples. This means stopping distance more than doubles. Be prepared to use this in calculations.

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