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

IA idea · Sport

Is there a limit to how fast humans can run 100 m?

AA SLAA HLAI SLAI HL Solid Also in: Modelling, Statistics

Research question

Which model — linear, exponential decay to an asymptote, or logistic — best fits the progression of the men's (or women's) 100 m world record, and what limiting time does it predict?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Records keep falling, but more slowly. Fitting models with an asymptote gives a predicted “ultimate” time — and discussing whether that prediction means anything is excellent Reflection.

The mathematics you'll need

Exponential and logistic models with asymptotes
Least-squares fitting with technology
Residuals and model comparison
Extrapolation and its limits

Modelling the data, step by step

This idea usually needs exponential or logistic models. See it worked step by step, with a criterion tip at every step: Exponential y = a e^(kx) + c and y = a·bˣ · Logistic y = L/(1 + C e^(−kx)) · Choosing and comparing models.

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

Record progression data from World Athletics or Olympic results from Olympedia.

World Athletics records and results — All-time lists, records and progression for every athletics event.
Olympedia — Complete Olympic results for every event since 1896.

Real data for this idea

Primary source: World Athletics records and toplists: All-time toplists. Opens on the men's 100 m: choose your event, copy the marks you need into your own table and cite the page and date. Licence: No reuse licence found: link and cite only.
Also useful: Olympedia results. Use the event result pages; copy only the rows you need and cite each page. Licence: No reuse licence found: link and cite only.

There is no open reuse licence for these figures: copy only the values you analyse into your own table, and cite the page and the date. Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Explain why records should approach a limit.
Fit several models.
Compare fits and predicted limits.
Test with data held back (recent records).
Reflect on timing technology, doping and footwear.

Pitfalls that cost marks

Linear extrapolation to absurd times.
Treating the record as a smooth function of time.
Ignoring hand-timed early records.

Showing personal engagement

Choose an event you compete in.
Compare men's and women's limits.
Discuss what the model says about the athletes of the future.

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	Exponential and logistic models with asymptotes; Least-squares fitting with technology
AA HL	Good fit	Exponential and logistic models with asymptotes; Least-squares fitting with technology
AI SL	Good fit	Exponential and logistic models with asymptotes; Least-squares fitting with technology
AI HL	Good fit	Exponential and logistic models with asymptotes; Least-squares fitting with technology

Level: Solid. Needs some independent work beyond class examples. 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: linear extrapolation to absurd times; and treating the record as a smooth function of time. Say how each one affects your answer.

Use of mathematics (E)

SL: exponential and logistic models with asymptotes; least-squares fitting with technology; residuals and model comparison; extrapolation and its limits, each explained in your own words and carried out correctly.

How sport explorations reach the top bands in general: Sport IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Fit models to the top-10 performances each year instead of the record alone and compare.

Extending it for HL

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

See a complete IA, marked

How long does a skydiver take to reach terminal velocity? (AA HL) is a complete sport exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL, AA HL, AI SL and AI HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Exponential and logistic models with asymptotes, least-squares fitting with technology, residuals and model comparison and extrapolation and its limits.

Where can I get data for this IA?

Record progression data from World Athletics or Olympic results from Olympedia. Checked sources and tools: World Athletics records and toplists, Olympedia and World Athletics records and results.

Turn this idea into your IA

The planner opens with “Is there a limit to how fast humans can run 100 m?” filled in: the question, the maths and the data sources.

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