IA idea · Kinematics & physics-style modelling

How fast does a sledge go? Acceleration, friction and slope

AA SLAI SLAA HL Solid Also in: Modelling, Sport

Research question

From videos of a sledge (or a skateboard, or a box on a ramp) on slopes of different angles, how does the acceleration depend on the angle, and what coefficient of friction does a model give?

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

Free: the A–E checklist an examiner uses, by email ↓

Why it makes a good exploration

Real motion on real slopes with a model to test. Estimating a physical parameter from fitted data, and judging whether it is constant, is good mathematics.

The mathematics you'll need

Constant-acceleration models
Quadratic fits to position data
Model a = g(sin θ − μ cos θ) fitted to several angles
Linearising to estimate μ
Residuals and parameter uncertainty

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 runs on measured slopes (or a ramp in school with a box or skateboard) and track them; measure angles with a clinometer.

Tracker video analysis — Free tool to track an object frame by frame in a video and export its x–y coordinates.
phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.
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 runs at several angles.
Fit position against time for each.
Fit the friction model across angles.
Check whether μ is constant.
Reflect on air resistance and surface changes.

Pitfalls that cost marks

Too few angles to test the model.
Unsafe runs; use a small ramp if in doubt.
Assuming μ is constant without checking.

Showing personal engagement

Use your own sledge or board.
Compare surfaces.
Predict the speed at the bottom of a longer slope and test it.

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	Constant-acceleration models; Quadratic fits to position data
AA HL	Good fit	Constant-acceleration models; Quadratic fits to position data
AI SL	Good fit	Constant-acceleration models; Quadratic fits to position data
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: 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

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: too few angles to test the model — 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 air resistance and compare the models on long runs.

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).