The goals of this activity are for students to understand the relationships between displacement, velocity, and acceleration. They also fit a polynomial model to experimental data. Students use the model to determine velocity and acceleration. The activity also provides historical context about Galileo's inclined-plane experiments and the Apollo 15 demonstration of a falling hammer and feather.

The experiment is implemented as a MATLAB live script that requires no programming.

This activity was designed as a virtual physics laboratory exercise for an online introductory physics course. It is intended for first-year university physics students and should take approximately one hour to complete.

No previous MATLAB experience or specialized technical skills are expected. Students are guided through the process of analyzing video-based motion data, converting measurement units, creating graphs, fitting polynomial models, and interpreting velocity and acceleration.

Although designed for an online laboratory, the activity can be adapted for use as an in-person classroom activity, a computer-based laboratory exercise, or a homework assignment. It could also be divided into shorter sections and completed across multiple class sessions.

The activity is structured as a MATLAB LiveScript for students to complete independently. No programming experience is required and the script has embedded controls. For the first section, students use an interactive cursor to determine the position of a ball rolling down a ramp in successive video frames and then plot position, velocity and acceleration. The exercise is repeated using video of the Apollo 15 demonstration of a hammer and feather being dropped on the Moon.
Gravitational Acceleration MATLAB LiveScript (MATLAB Live Script 1.8MB Sep25 26)
Rolling Ball Data (Matlab .MAT File 56.6MB Sep25 26)
Apollo Experiment Data (Matlab .MAT File 28.1MB Sep25 26)
Activity Follow-up Questions (Acrobat (PDF) 72kB Sep25 26)
Example output from activity (Acrobat (PDF) 2.8MB Sep25 26)

It can be helpful to remind students to check that the current directory for MATLAB is set to the folder containing the script and both data files or they will encounter errors due to the mat files not being found.

The students are expected to complete the MATLAB activity independently and submit a PDF showing completion. Assessment is based on a set of follow-up questions.

Historical and experimental background on Galileo's inclined-plane investigations.

Straulino, S. (2008). Reconstruction of Galileo Galilei's experiment: The inclined plane. Physics Education, 43(3), 316–321.
https://doi.org/10.1088/0031-9120/43/3/012

Background, video, and source information for the Apollo 15 demonstration.

NASA. Apollo 15 Hammer-Feather Drop.
https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html

Primary source describing the hammer, feather, release height, and experimental observation.

Allen, J. P. (1972). Summary of scientific results. In Apollo 15 preliminary science report (NASA SP-289). National Aeronautics and Space Administration.
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720015164.pdf