Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

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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)

Modelling the data, step by step

This idea usually needs a quadratic model. See it worked step by step, with a criterion tip at every step: Quadratic: three points, completing the square, regression.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for 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.

Real data for this idea

Primary source: GOV.UK rates and thresholds: The Highway Code, rule 126: typical stopping distances. Take the thinking and braking distances at each speed from 20 to 70 mph. Licence: Open Government Licence v3.0.

Links checked October 2026; we link to the data and never copy it. More free data sets.

Ready to use: Stopping distances in the IA data bank — cited, licensed for reuse, and one click to open in the grapher.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Linear and quadratic models; Separating a function into two components
AA HL	Not a natural fit	The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E.
AI SL	Good fit	Linear and quadratic models; Separating a function into two components
AI HL	Not a natural fit	The mathematics is mainly from the AA course; an AI HL version would need modelling with technology, statistics or networks at HL level.

Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: mixing miles, metres and seconds; and fitting one quadratic to total distance and missing the two-part structure. Say how each one affects your answer.

Use of mathematics (E)

SL: linear and quadratic models; separating a function into two components; least-squares fitting and interpreting coefficients; unit conversion and kinematics (v² = 2as), each explained in your own words and carried out correctly.

How modelling explorations reach the top bands in general: Modelling with functions IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

Add an HL technique the question genuinely needs: what an HL modelling exploration adds.

See a complete IA, marked

Is a hanging chain a parabola? Comparing catenary and quadratic models (AA SL) is a complete modelling exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL and AI SL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Linear and quadratic models, separating a function into two components, least-squares fitting and interpreting coefficients and unit conversion and kinematics (v² = 2as).

Where can I get data for this IA?

Use the published thinking and braking distances for 20–70 mph; optionally measure your own reaction time with an online test or phyphox. Checked sources and tools: GOV.UK rates and thresholds, The Highway Code (GOV.UK), rule 126 and phyphox (RWTH Aachen).

Turn this idea into your IA

The planner opens with “Why do stopping distances grow so fast? Modelling the Highway Code table” filled in: the question, the maths and the data sources.

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