Stopping Distances (AQA GCSE Combined Science: Synergy: Physical Sciences): Revision Note

Exam code: 8465

Thinking & Braking Distances

  • The stopping distance of a car is defined as:

    The total distance travelled during the time it takes for a car to stop in response to some emergency

  • It can be written as an equation involving two distances:

Stopping distance = Thinking distance + Braking distance

  • Where:

    • Thinking distance = the distance travelled in the time it takes the driver to react (reaction time) in metres (m)

    • Braking distance = the distance travelled under the braking force in metres (m)

    • Stopping distance = the sum of the thinking distance and braking distance, in metres (m)

  • For a given braking force, the greater the speed of the vehicle, the greater the stopping distance

Worked Example

At a speed of 20 m/s, a particular vehicle had a stopping distance of 40 metres. The car travelled 14 metres whilst the driver was reacting to the incident in front of him. What was the braking distance?

A. 54 m

B. 34 m

C. 26 m

D. 6 m

Answer: C

Step 1: Identify the different variables

  • Stopping distance = 40 m

  • Thinking distance = 14 m

Step 2: Rearrange the formula for stopping distance

Stopping distance = Thinking distance + Braking distance

Braking distance = Stopping distance – Thinking distance

Step 3: Calculate and identify the correct braking distance

  • Braking distance = 40 – 14 = 26 metres

  • Therefore, the answer is C

Factors Affecting Stopping Distance

  • The thinking distance is defined as:

    The distance travelled by a car from when a driver realises they need to brake to when they apply the brakes

  • The reaction distance is equal to:

Reaction Distance = Speed of the car × Driver’s reaction time

Factors affecting thinking distance

  • The main factor that affects the thinking distance is the car’s speed, however additional factors can affect the thinking distance

  • It is increased by:

    • Tiredness

    • Distractions (e.g. using a mobile phone)

    • Intoxication (i.e. consumption of alcohol or drugs)

  • Since these factors can affect the driver's reaction time, they directly affect the thinking distance

Factors affecting braking distance

  • The braking distance is the distance a vehicle travels from when the brakes are applied until the vehicle stops

  • The main factor affecting braking distance is the vehicle's speed

    • The greater the speed, the greater the braking distance

  • Additional factors that increase the braking distance include:

    • Adverse road conditions: wet or icy roads reduce friction between the tyres and the road surface

    • Poor tyre condition: worn tyres have reduced grip, decreasing the friction force available

    • Poor brake condition: worn or faulty brakes reduce the braking force that can be applied

Worked Example

The graph below shows how the thinking distance of a driver depends on the speed of the car.

Graph showing thinking distance (m) on the y-axis against speed (m/s) on the x-axis, with a straight line through the origin showing that thinking distance is directly proportional to speed

(a) Describe the connection between thinking distance and speed.

(b) Some people drive when they are tired, despite warnings against doing so. Draw a new line on the graph to show how thinking distance varies with speed for a tired driver.

Answer:

Part (a)

Step 1: Check if the line is straight and if it goes through the origin

  • The graph shows a straight line through the origin

  • Therefore, the thinking distance is directly proportional to the speed of the car

Part (b)

Step 1: Recall the factors which affect the thinking distance

  • Three additional factors affect the thinking distance, because they affect human reaction time:

    • Tiredness

    • Distractions

    • Intoxication

  • Hence, a tired driver's reaction time is greater (i.e. it takes longer for them to react)

Step 2: Draw a line that shows greater thinking distance for the same speed

  • At the same speed, a tired driver's thinking distance will be greater than a driver who is alert

  • This means a line should be drawn with a steeper gradient, as shown below:

The same thinking distance vs speed graph with a second steeper straight line added through the origin, representing a tired driver whose greater reaction time results in a larger thinking distance at every speed

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