Stopping Distance
Master Stopping Distance for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Stopping distance is the sum of the thinking distance and the braking distance, both of which increase with speed.
Free downloads
These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
The stopping distance of a vehicle is the sum of the thinking distance and the braking distance.
Thinking distance is the distance travelled during the driver's reaction time, before the brakes are applied. Braking distance is the distance travelled while the braking force is slowing the vehicle down.
Increasing speed increases both, but not equally. Thinking distance is directly proportional to speed, because reaction time is unchanged. Braking distance increases with the square of the speed, because the kinetic energy is proportional to speed squared and all of it must be transferred by the braking force. Doubling the speed doubles the thinking distance but quadruples the braking distance.
Revision notes
The two components
Stopping distance = thinking distance + braking distance.
Thinking distance is the distance travelled during the driver's reaction time. Braking distance is the distance travelled while the braking force slows the vehicle to a stop.
Effect of speed
Thinking distance is directly proportional to speed, because the reaction time does not change.
Braking distance increases with the square of the speed, because kinetic energy is proportional to speed squared and all of it must be transferred by the braking force. Doubling the speed quadruples the braking distance.
Why it matters
The sharp increase in braking distance with speed is why speed limits exist and why they matter disproportionately.
A small increase in speed produces a much larger increase in overall stopping distance, particularly at higher speeds.
Key points
- Stopping distance = thinking distance + braking distance.
- Thinking distance is travelled during the reaction time.
- Braking distance is travelled while decelerating.
- Thinking distance is proportional to speed.
- Braking distance is proportional to speed squared.
- Doubling speed quadruples the braking distance.
Worked examples
Example 1
A vehicle has a thinking distance of 12 m and a braking distance of 24 m. Calculate the stopping distance. [2 marks]
Model answer
Stopping distance = thinking distance + braking distance = 12 + 24 (1 mark) = 36 m (1 mark).
Example 2
Explain why doubling the speed of a car more than doubles its stopping distance. [3 marks]
Model answer
The thinking distance doubles, because it is directly proportional to speed (1 mark). The braking distance quadruples, because it increases with the square of the speed (1 mark). The total stopping distance therefore increases by more than double (1 mark).
Example 3
Explain why braking distance increases with the square of the speed. [2 marks]
Model answer
The kinetic energy of the vehicle is proportional to the square of its speed (1 mark), and all of that energy must be transferred by the work done by the braking force, so a greater distance is needed (1 mark).
Common mistakes
Saying both distances double when speed doubles.
Thinking distance doubles but braking distance quadruples.
Confusing thinking and braking distance.
Thinking is before the brakes are applied; braking is after.
Forgetting to add the two together.
Stopping distance is the sum of both.
Not linking braking distance to kinetic energy.
The squared relationship comes from kinetic energy being proportional to speed squared.
Exam tips
- Always give stopping distance as the sum of both parts.
- State the different effects of speed on each part.
- Explain the squared relationship through kinetic energy.
- Use the proportionalities precisely in explanations.
Key terms
- Stopping distance
- Thinking distance plus braking distance.
- Thinking distance
- Distance travelled during the reaction time.
- Braking distance
- Distance travelled while the brakes slow the vehicle.
- Reaction time
- The time between seeing a hazard and applying the brakes.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.