Stopping Distance (Oxford AQA IGCSE Physics)

Revision Note

Stopping Distance

  • 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

  • Stopping distance is the sum of the thinking distance and the braking distance

Stopping distance = Thinking distance + Braking distance

Thinking distance

  • Thinking distance is defined as:

The distance travelled in the time it takes the driver to react (reaction time) in metres (m)

  • The main factors affecting thinking distance are:

    • The speed of the car

    • The reaction time of the driver 

  • The reaction time is defined as:

A measure of how much time passes between seeing something and reacting to it

  • The average reaction time of a human is 0.25 s

  • Reaction time is increased by:

    • Tiredness

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

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

Braking distance

  • Braking distance is defined as:

The distance travelled under the braking force in metres (m)

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

The effect of speed on stopping distance

A chart showing stopping distances at different speeds. The thinking distance increases linearly with speed, but the breaking distance increases at an increasing rate with speed.
A vehicle's stopping distance increases with speed. At a speed of 20 mph the stopping distance is 12 m, whereas at 60 mph the stopping distance is 73 m (reproduced from the UK Highway Code)

A Table Showing Speed and Stopping Distance

Speed (mph)

Speed (m/s)

Stopping Distances (m)

20

9

12

30

14

23

40

18

36

50

22

53

60

27

73

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 them.

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

braking distance = 26 metres

Therefore, the answer is C

Worked Example

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

Graph showing thinking distance increases with speed. The graph is a straight line that goes through the origin.

(a) Use the graph to describe the relationship 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 graph now shows a second line for a tired driver which is steeper than the first line. At a speed of 20 metres per second, the thinking distance is greater for the tired driver than it is for the alert driver

Factors Affecting Braking Distance

  • The main factor affecting the braking distance of a car is its speed

  • There are additional factors which affect the braking distance, such as:

    • Vehicle condition - e.g. worn tyres or poor brakes

    • Road condition - wet or icy roads make it harder to decelerate

    • Vehicle mass - a heavy vehicle, such as a lorry, takes longer to stop

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