Mathematics 11–12 · Years 11–12

Free fall on video: displacement, velocity and acceleration from frames

Introduction to differentiation: The derivative as a rate of change (Mathematics Advanced, Year 11); Applications of calculus: Rates of change (Mathematics Advanced, Year 12)

Practical, model not builtLow risk

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The idea

Velocity is the derivative of displacement and acceleration the derivative of velocity, and a dropped ball filmed at a known frame rate gives all three from real positions.

What you need

A phone camera recording at 30 or 60 frames per second (check the setting)
A tennis ball
A metre rule taped to a wall as the scale, a plain background
Tracker video analysis software (Open Source Physics, free) on a laptop

How to do it

Film the ball released from rest beside the metre rule, camera level and 2 m back; three drops of 1.00 m.
In Tracker set the scale from the metre rule and the origin at the release point; mark the ball's centre in each frame until it lands.
Export the (t, s) table, plot s against t and fit s = a t^2; record a for each drop.
Compute velocity between successive frames as the change in s divided by the frame interval, plot v against t and find the gradient.
Compare the fitted a with g/2 = 4.90 m/s^2 and the velocity gradient with g = 9.80 m/s^2; state the percentage difference.

What you should see

With g = 9.80 m/s^2, s = 4.90 t^2 gives 0.441 m at 0.30 s and 0.784 m at 0.40 s; a 1.00 m fall takes 0.452 s and ends at 4.43 m/s. At 30 frames per second the fall spans 13 frame intervals, at 60 frames per second 27, so the higher frame rate gives twice as many points for the fit. The velocity-time graph is a straight line through the origin of gradient 9.8 m/s^2. The learner knows it worked when the position fit is quadratic with an intercept close to zero and the velocity plot is linear.

What changes

What you change: time since release
What you measure: displacement and velocity of the ball
What you keep the same: release from rest
same ball
camera perpendicular to the fall and not moved between drops
scale set from the same rule

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

A heavier ball falls faster; over 1 m the effect of air resistance on a tennis ball is too small to see between frames.
Constant acceleration means constant velocity; the velocity grows linearly while the acceleration stays fixed.
The speed is read from the s-t graph as a height; it is the gradient of the tangent, in metres per second.

Safety card

Low riskLearners carry it out

Hazards

ball rolling into a walkway

Controls

drop onto a mat or catch below the field of view

Note

No chemicals and no heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics Advanced 11–12 Syllabus (2024), Year 11 focus area Introduction to differentiation; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-11-06
Mathematics Advanced 11–12 Syllabus (2024), Year 12 focus area Applications of calculus; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-12-06
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

All Concept Studio activities