1. Find the fictional total at 20 m/s.
- Thinking: 20×1=20 m.
- Braking: 0.05×20²=20 m.
- Total: 20+20=40 m.
Maths · Suggested Classes 6–8
Road Safety Week 2026: Stopping-Distance Maths Activity
Double the speed in a model and the stopping distance need not simply double. Separate what happens before braking from what happens during braking.
Start here
UK Road Safety Week 2026 is 15–21 November. This paper-only maths activity uses a fictional model to compare thinking, braking and total stopping distances.
Original BananaLearn guide · 7 November 2026
On a narrow screen, swipe the diagram or open it full size.
Find a section, worked example or practice question
Dates and purpose
Brake’s UK Road Safety Week runs from 15 to 21 November 2026. This is an independent BananaLearn learning activity, not Brake’s official action pack. Use the organiser’s site for campaign materials and current messages.
The calculations below are fictional teaching values, not official stopping-distance guidance or predictions for a real vehicle. Complete the task with paper, diagrams and supplied data; no live-road experiment is part of it.
Name the two stages
Thinking distance is distance travelled during the model’s reaction interval before braking begins. Braking distance is distance travelled during braking until rest. Total stopping distance is their sum.
A diagram should begin both bars at the same starting reference and show the stage boundary. “The brakes act instantly” would remove the first stage and change the model.
Define a transparent classroom model
Let speed v be in metres per second. Assume reaction interval t=1 second and fictional braking rule b=0.05v² metres. Thinking distance is vt=v metres, so total d=v+0.05v².
These assumptions are chosen for arithmetic and comparison. Real stopping depends on many conditions, including reaction, road surface, tyres, brakes and gradient. Do not use the model to decide whether a real road situation is safe.
On a narrow screen, swipe the diagram or open it full size.
Complete the supplied table
At v=10 m/s, thinking distance is 10 m, braking distance 5 m and total 15 m. At 20 m/s, they are 20,20 and 40 m. At 30 m/s, they are 30,45 and 75 m.
Label every column and keep the squared speed in brackets before multiplying. The totals are sums of distances; a speed value cannot be added directly to a distance without using the model’s time and coefficient units.
Explain what doubling does
Doubling v doubles vt when the reaction interval stays fixed. In the braking rule, (2v)²=4v², so braking distance quadruples. Total distance combines these two changes.
From 10 to 20 m/s, total distance rises from 15 to 40 m: a factor of 8/3, not 2 or 4. Do not apply the braking factor to the total without recalculating both parts.
Change one assumption at a time
Keep v=20 m/s and change the model reaction interval from 1 to 1.5 seconds. Thinking distance becomes 30 m; braking remains 20 m; total becomes 50 m.
This comparison isolates the reaction interval. If speed and braking coefficient also changed, you could still calculate the new total, but you could not attribute its whole increase to one factor.
Draw proportional stacked bars
Use one scale for all distances and a consistent colour or pattern for each stage. A 75 m total bar must be five times the length of a 15 m total bar. Put the units and “fictional model” beside the chart.
A drawing of a car is a visual cue, not a scale vehicle. Avoid stretching an illustration to suggest a measurement. The stacked distance bars carry the quantitative information.
Use evidence in a short explanation
Complete: “Under this model, increasing speed from ___ to ___ changes thinking distance from ___ to ___ and braking distance from ___ to ___. Therefore the total changes from ___ to ___.”
Then state one limitation. The activity’s useful outcome is explaining a non-linear relationship and reading a model honestly. It does not supply personal driving advice, legal requirements or a certified safe distance.
See the reasoning
Worked examples and checks
2. Find the fictional total at 20 m/s with a 1.5-second reaction interval.
- Thinking: 20×1.5=30 m.
- Braking stays 20 m because its assumed rule has not changed.
- Total: 50 m, an increase of 10 m.
3. Explain why 30 m/s gives 75 m in this model.
- Thinking is 30 m; braking is 0.05×900=45 m.
- Adding gives 75 m.
- Compared with 10 m/s, speed triples, thinking triples and braking becomes nine times as large.
Try, explain, check
12 questions with explained answers
Try each task before opening its explanation. These are original BananaLearn questions, not official exam or past-paper questions. Where several answers can work, the explanation gives the criteria.
What are the UK campaign dates?
Check answer and reasoning
15–21 November 2026
The organiser confirms those dates.Is this an official stopping-distance table?
Check answer and reasoning
No
Its values come from a stated fictional classroom model.At 10 m/s, what is thinking distance for t=1 s?
Check answer and reasoning
10 m
vt=10×1.At 10 m/s, what is model braking distance?
Check answer and reasoning
5 m
0.05×10²=5.What is the total at 10 m/s?
Check answer and reasoning
15 m
10+5.What is the total at 30 m/s?
Check answer and reasoning
75 m
30+0.05×900.When speed doubles, how does this model’s braking distance change?
Check answer and reasoning
It quadruples
The speed is squared.Does the total necessarily quadruple too?
Check answer and reasoning
No
The thinking component changes linearly.At 20 m/s, how far is travelled in an extra 0.5 s before braking?
Check answer and reasoning
10 m
20×0.5=10.Name a fair graph requirement.
Check answer and reasoning
For example: a shared distance scale and clearly labelled stage segments
The visual must preserve quantitative comparisons.Name a real-world factor the simple model holds out.
Check answer and reasoning
For example: road surface, gradient or tyre condition
Actual conditions affect stopping behaviour.Should children test the model on a live road?
Check answer and reasoning
No
It is a paper-and-supplied-data task.
A checking record to use in your notebook
Copy these headings and fill them for one worked task, then for a fresh attempt. Use your own evidence rather than copying the model answer.
- Date and setting
- What is confirmed, and which example is fictional?
- Task and conditions
- Which rule, quantity, passage or clue is supplied?
- Plan or answer
- What will I calculate, say or change?
- Evidence
- How can another reader check the reasoning?
- Revision
- What would I change after a trial or rehearsal?
Choose the next useful step
Explore BananaLearn’s games, learning features and one-to-one tutoring. Maths is our priority; English and Science tutoring are also available. Bring a recent example of schoolwork when checking teaching fit.
Sources, level and update
Original BananaLearn explanations, examples, illustrations and practice. Source facts checked 7 November 2026. Suggested levels are learning guides, not a claim that every board or textbook uses the same sequence.
Event timing is calendar-backed. Search demand is a forecast unless a separately measured trend is stated. No official event theme, school programme or affiliation is implied.
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