The Graphs and Tracks Model is a highly influential interactive physics simulation designed to help students master one-dimensional kinematics by connecting real-world physical motion to abstract graphs. Originally developed in the 1980s by David Trowbridge at the University of Washington, it bridges the gap between what a student sees happening (a ball rolling) and what they see graphed (position, velocity, and acceleration curves).
The tool was a breakthrough in physics education research (PER), specifically addressing the common misconception where students interpret a graph as a literal, two-dimensional “picture” or map of the motion rather than a function of time. How the Simulation Works
The model operates on a puzzle-like setup split into two main core exercise modes:
From Graphs to Motion (The Matching Game): The software displays a target, dotted-line kinematic graph (such as position vs. time). The student must physically manipulate the height of various track segments and adjust the initial position and velocity of a ball until its rolled path perfectly traces over and matches the target graph.
From Motion to Graphs: The software shows a predetermined track setup and rolls the ball. The student is given a blank graph and digital sketching tools (lines, parabolas) to construct the position, velocity, or acceleration curves that accurately map the ball’s trajectory. Simplifying Assumptions (Idealizations)
To keep the mathematical focus strictly on core kinematics without cluttering the learning process with messy variables, the model uses a few intentional assumptions:
Sliding, Not Rolling: Even though the simulation refers to a “rolling ball”, the calculations behave like a sliding point mass to avoid the 29% reduction in acceleration caused by rotational kinetic energy.
Zero Friction: The ball slides without any friction or air resistance.
Exaggerated Slopes: The vertical dimension of the track is visually exaggerated on screen (up to nine times steeper) so students can easily see slight slopes, while the software calculates using small-angle physics.
No Bouncing: When the ball passes over a sharp angle where two track segments meet, the transition is calculated as artificially smooth so the ball never flies off the track. Modern Access and Alternatives
While the 1980s original was distributed via Physics Academic Software, modern physics education relies on highly accessible, updated iterations: Graphs and Tracks Graphs and Tracks
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