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Physics · Forces

Stopping distance and reaction time

Define stopping distance as thinking distance plus braking distance, describe factors affecting reaction time, and use \(s = vt\) for thinking distance.

  • 6 key terms
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Warm-up

Answer each one, then check.

  1. 1

    What is speed?

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    Distance divided by time

  2. 2

    What is distance = speed × time?

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    \(s = vt\)

  3. 3

    What is reaction time?

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    The time between seeing something and reacting

  4. 4

    What does braking do?

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    Reduces the vehicle's kinetic energy

  5. 5

    What is a typical human reaction time?

    Show answerHide answer

    0.2 s to 0.9 s

Learning Objectives

  1. 1Define stopping distance, thinking distance and braking distance.
  2. 2Explain how speed affects stopping distance.
  3. 3Describe factors that affect reaction time, and methods used to measure it.
  4. 4Interpret graphs relating speed to stopping distance.

STOPPING DISTANCE

stopping distance = thinking distance + braking distance

Thinking distance is the distance travelled during the driver's reaction time. Braking distance is the distance travelled under the braking force. For a given braking force, the greater the speed, the greater the stopping distance.

Reaction Time

Typical values and factors.

  • Typical reaction time

    Detail: 0.2 s to 0.9 s

  • Increases with

    Detail: Tiredness, drugs, alcohol, distractions such as a mobile phone

  • Thinking distance

    Detail: \(s = vt\): reaction time × speed

  • Measuring it

    Detail: Ruler drop test: the distance the ruler falls gives the reaction time

Thinking Distance

A driver travelling at 15 m/s has a reaction time of 0.60 s. Calculate the thinking distance.

Show the solutionHide the solution
  1. 1 Write the equation \(s = vt\)
  2. 2 Substitute \(s = 15 \times 0.60\)
  3. 3 Answer \(s = 9.0\) m

Answer9.0 m

Stopping Distance

A car has a thinking distance of 9.0 m and a braking distance of 14 m. Calculate the stopping distance.

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  1. 1 Add \(9.0 + 14 = 23\) m

Answer23 m

Measuring Reaction Time

Describe the ruler drop method.

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  1. 1 Set up A partner holds a ruler vertically with the zero between your thumb and finger
  2. 2 Drop Without warning they drop it, and you catch it as fast as you can
  3. 3 Measure The distance fallen is read from the ruler
  4. 4 Convert Use a table of distance against time, then repeat and find a mean

AnswerThe longer the distance the ruler falls, the longer the reaction time.

Distractions

Explain the effect of a driver texting on the stopping distance.

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  1. 1 Reaction time Increases
  2. 2 Thinking distance \(s = vt\) is greater
  3. 3 Stopping distance So the total stopping distance is greater

AnswerA longer reaction time gives a longer thinking distance and so a longer stopping distance.

Why It Matters

Safety.

  • Speed limits

    Higher speed means a much greater stopping distance.

  • Driver factors

    Tiredness, alcohol, drugs and distractions raise reaction time.

  • Estimates

    Estimate how emergency stopping distance varies over typical speeds.

  • Graphs

    Interpret graphs of speed against stopping distance for different vehicles.

Reaction Test

In a ruler drop test a student's three results for the distance fallen are 14 cm, 16 cm and 15 cm. Calculate the mean. Explain why a tired driver would have a longer stopping distance.

1. Find the mean.

2. Link to s = vt.

A good answer shows: Mean = 15 cm. Tiredness increases reaction time, so thinking distance increases, increasing the stopping distance.

Can I...?

  1. 1Define stopping distance.
  2. 2Define thinking and braking distance.
  3. 3Use s = vt.
  4. 4List factors affecting reaction time.
  5. 5Describe a reaction-time test.
  6. 6Read a stopping distance chart.
  7. 7Explain the effect of speed.
  8. 8Estimate stopping distances.

Summary & Exam Focus

  • Stopping = thinking + braking.
  • Thinking distance: \(s = vt\).
  • Reaction time 0.2 to 0.9 s; increased by tiredness, drugs, alcohol, distractions.
  • Higher speed gives a greater stopping distance.

Exam focus

A driver travels at 15 m/s with a reaction time of 0.60 s. Calculate the thinking distance. (2 marks) (2 marks)

Multiply speed by reaction time.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Stopping distance
Thinking distance plus braking distance.
Thinking distance
Distance travelled in the driver's reaction time.
Braking distance
Distance travelled while the brakes slow the vehicle.
Reaction time
The time between a stimulus and a response.
Distraction
Something that takes a driver's attention away.
Mean
The average of repeated readings.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    A car travels at 15 m/s. The driver's reaction time is 0.60 s. Calculate the thinking distance. Use the equation: distance = speed × time

    Show answerHide answer

    Model answer

    \(15 \times 0.60 = 9.0\) m

    Mark scheme

    • Correct substitution — 1 mark
    • 9.0 m — 1 mark
  2. Question 2 State 2 marks

    Give two factors that can increase a driver's reaction time.

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    Model answer

    Any two from: tiredness, alcohol, drugs, distractions (such as using a mobile phone).

    Mark scheme

    • First factor — 1 mark
    • Second factor — 1 mark
  3. Question 3 Use the chart 4 marks

    The chart shows the thinking distance and braking distance for a car at different speeds. (a) Use the chart to find the stopping distance at 50 mph. (b) Describe how the thinking distance changes with speed. (c) Explain why the braking distance increases more quickly than the thinking distance.

    A stacked bar chart of thinking distance and braking distance for speeds from 20 to 70 miles per hour.
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    Model answer

    (a) About 53 m. (b) The thinking distance is directly proportional to the speed (it increases by equal amounts). (c) The braking distance depends on the kinetic energy of the car, which increases with the square of the speed.

    Mark scheme

    • 53 m — 1 mark
    • Thinking distance increases steadily or proportionally — 1 mark
    • Braking distance depends on kinetic energy — 1 mark
    • Kinetic energy ∝ speed² — 1 mark
  4. Question 4 Explain 3 marks

    A driver is sending a text message while driving. Explain how this affects the stopping distance of the car.

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    Model answer

    The driver's attention is on the phone so their reaction time is longer. Thinking distance = speed × reaction time, so the thinking distance increases and the stopping distance is greater.

    Mark scheme

    • Reaction time increases — 1 mark
    • Thinking distance increases — 1 mark
    • Stopping distance greater — 1 mark
  5. Question 5 Describe 4 marks

    Describe an experiment to measure a person's reaction time using a ruler. Explain how the result is used.

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    Model answer

    A partner holds a ruler vertically with zero level with the person's thumb and finger. The ruler is dropped without warning and caught. The distance fallen is read off and converted to a time (from a table or calculation). The test is repeated and a mean found; different conditions (distractions) can be compared.

    Mark scheme

    • Ruler held and dropped without warning — 1 mark
    • Distance fallen measured — 1 mark
    • Converted to a reaction time — 1 mark
    • Repeat and mean, compare conditions — 1 mark

Quick check

  1. Stopping distance is...

    1. Athinking × braking
    2. Bthinking distance + braking distance
    3. Cbraking − thinking
    4. Dspeed ÷ time
    Show answerHide answer

    B: thinking distance + braking distance

    The sum of the two.

  2. A typical reaction time is...

    1. A2 s to 9 s
    2. B0.02 s
    3. C0.2 s to 0.9 s
    4. D20 s
    Show answerHide answer

    C: 0.2 s to 0.9 s

    Typical human range.

  3. Which does NOT increase reaction time?

    1. ATiredness
    2. BAlcohol
    3. CUsing a phone
    4. DDrinking water
    Show answerHide answer

    D: Drinking water

    Water is not a cause.

  4. A longer reaction time gives a...

    1. Agreater thinking distance
    2. Bsmaller thinking distance
    3. Cno change
    4. Dsmaller braking force
    Show answerHide answer

    A: greater thinking distance

    s = vt.

  5. At higher speed the stopping distance is...

    1. Asmaller
    2. Bgreater
    3. Cthe same
    4. Dzero
    Show answerHide answer

    B: greater

    Both components increase.

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