How fast is a sprinter at each moment? Differentiating 100 m splits

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

Research question

Can a model of distance against time fitted to 10 m split times estimate a sprinter's top speed and when it is reached, and how does my own sprint compare?

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

Why it makes a good exploration

Split times record distance at each 10 m, but not speed. Fitting a model and differentiating it recovers the velocity curve — then you can compare an elite race with your own sprint filmed on a phone.

The mathematics you'll need

Fitting a model such as d(t) = v_max(t − τ(1 − e^(−t/τ)))
Differentiation to find velocity and acceleration
Least squares or parameter estimation
Comparing parameters across athletes

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

Film your own 60 m sprint with markers every 10 m and read times; published elite split times exist in biomechanics reports from major championships.

Tracker video analysis — Free tool to track an object frame by frame in a video and export its x–y coordinates.
World Athletics records and results — All-time lists, records and progression for every athletics event.

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

Explain why a sprinter's speed rises then levels off.
Fit a model to split data.
Differentiate to get velocity and find top speed.
Compare your own sprint with an elite race.
Reflect on reaction time and deceleration at the end.

Pitfalls that cost marks

Using average speed over a split as instantaneous speed without comment.
Choosing a polynomial that behaves badly outside the data.
Ignoring the reaction time at the start.

Showing personal engagement

Race yourself and friends with consent, filming carefully.
Predict your 100 m time from your 60 m model.
Compare two different training sessions.

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

Taking it further

Fit the model to several elite athletes and compare the acceleration constant τ; relate it to body mass or event specialism.

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).