Why do stopping distances grow so fast? Modelling the Highway Code table

AA SLAI SL Accessible Also in: Calculus, Statistics

Research question

Can the UK Highway Code's typical stopping distances be explained by a linear thinking distance plus a quadratic braking distance, and what does the model imply about reaction time and deceleration?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Every learner driver memorises the table, but few notice that it is built from a simple physical model. Recovering that model — and questioning it — is a clean, satisfying IA with real consequences for road safety.

The mathematics you'll need

Linear and quadratic models
Separating a function into two components
Least-squares fitting and interpreting coefficients
Unit conversion and kinematics (v² = 2as)

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Use the published thinking and braking distances for 20–70 mph; optionally measure your own reaction time with an online test or phyphox.

The Highway Code (GOV.UK), rule 126 — The UK's published typical stopping distances (thinking + braking) from 20 to 70 mph.
phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Present the table and convert units carefully.
Fit thinking distance as a linear function of speed and interpret the gradient as a reaction time.
Fit braking distance as a quadratic and interpret the coefficient as a deceleration.
Compare with your own measured reaction time and with wet-road conditions.
Reflect on what the table assumes about drivers and cars.

Pitfalls that cost marks

Mixing miles, metres and seconds.
Fitting one quadratic to total distance and missing the two-part structure.
Presenting the table as measured data (it is a model).

Showing personal engagement

Measure reaction times of volunteers (with consent) and see how the thinking distance changes.
Recalculate the table for a phone-distracted driver.
Discuss whether 20 mph zones are justified by your model.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Model braking with speed-dependent friction or air resistance and see how much the quadratic changes at motorway speeds.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).