IA idea · Kinematics & physics-style modelling

Estimating g from a video of a falling ball

AA SLAI SL Accessible Also in: Modelling

Research question

How accurately can the acceleration due to gravity be found by fitting a quadratic to video-tracked positions of a falling ball, and how does the result depend on the ball, the frame rate and the fitting method?

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

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Why it makes a good exploration

A simple experiment with a known answer to compare with. The interest is in comparing fitting methods and finding where air resistance starts to matter.

The mathematics you'll need

Quadratic models s = ut + ½at²
Least-squares fitting and residuals
Finite differences for velocity
Comparing with the accepted value; percentage error
Effect of frame rate on accuracy

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.

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 · 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

Film drops against a measured scale and track them in Tracker; use balls of different mass and size.

Tracker video analysis — Free tool to track an object frame by frame in a video and export its x–y coordinates.
Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

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

Film and track several drops.
Fit quadratics and extract g.
Compare with finite-difference estimates.
Compare balls and frame rates.
Reflect on air resistance and scale errors.

Pitfalls that cost marks

A scale not in the plane of the fall.
Too few frames.
Only one drop per ball.

Showing personal engagement

Choose balls from your own sport.
Predict which ball gives the worst estimate.
Film with slow-motion and compare.

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	Quadratic models s = ut + ½at²; Least-squares fitting and residuals
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	Quadratic models s = ut + ½at²; Least-squares fitting and residuals
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

Personal engagement (C)

Film or record the motion yourself, choose what to vary, and say what you expected before you analysed it.

Reflection (D)

Compare your model with the data and explain each mismatch (air resistance, friction, tracking error); reflect on how noise affects numerical derivatives. For this idea, start with: a scale not in the plane of the fall — say how it affects your answer.

Use of mathematics (E)

SL: Displacement, velocity and acceleration related by differentiation and integration, fitted models compared with residuals, and the physics assumptions turned into stated mathematical assumptions.

HL: Vectors for motion in two dimensions, a differential equation for a resisted motion solved and compared with data, or numerical differentiation with an error analysis.

Criteria A and B (presentation and communication) work the same way for every idea: see the guides to Criterion A and Criterion B.

Taking it further

Add a drag term and compare models for a light ball.

Extending it for HL

Add air resistance or friction as a differential equation, solve it (analytically or with Euler's method) and compare with the simpler model.

See a complete IA, marked

Our annotated exemplar How long does a skydiver take to reach terminal velocity? (AA HL) asks a different question, but shows how a complete kinematics exploration is structured and marked, with an examiner's comment on every criterion. Free excerpts and the full marking table are on its page.

Before you start: the checklist an examiner uses

Every check for Criteria A–E in a 4-page PDF, the mistakes that cost the most marks and a self-assessment grid. We'll email it with a short IA tip every few days, timed to your deadline if you give it. Free — no account, no payment.

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Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Criteria checklistCheck your plan or draft against the A–E descriptors and self-grade before you hand it in. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, an IB examiner, reads your draft and talks it through with you (€100).