This mobile-friendly simulation offers a highly interactive way for learners to explore how graphs of position vs. time or velocity vs. time are related to real-world motion. In each exercise, the simulation provides a motion graph. The student's task is to build a ramp with the correct height and incline angles so the motion of the rolling ball matches the target graph. Adjustments can be made until the ramp configuration is an accurate match. Built-in "star" rewards create a game-like environment with incentives to keep going.

Editor's Note: This activity could be useful as a formative assessment. It can be adapted for a variety of learning levels from conceptual physics through AP Physics courses. It's fun, but challenging.

When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. (9-12)

NGSS Science and Engineering Practices (K-12)

Developing and Using Models (K-12)

Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)

Use a model to provide mechanistic accounts of phenomena. (9-12)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

Create a computational model or simulation of a phenomenon, designed device, process, or system. (9-12)

Common Core State Standards for Mathematics Alignments

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^{?}

Linear, Quadratic, and Exponential Models^{?} (9-12)

F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

T. Henderson, Physics Classroom: Graphs and Ramps Interactive, (2018), <https://www.physicsclassroom.com/Physics-Interactives/1-D-Kinematics/Graphs-and-Ramps>.

Henderson, T. (2018, July 31). Physics Classroom: Graphs and Ramps Interactive. Retrieved September 16, 2021, from https://www.physicsclassroom.com/Physics-Interactives/1-D-Kinematics/Graphs-and-Ramps

%0 Electronic Source %A Henderson, Tom %D July 31, 2018 %T Physics Classroom: Graphs and Ramps Interactive %V 2021 %N 16 September 2021 %8 July 31, 2018 %9 text/html %U https://www.physicsclassroom.com/Physics-Interactives/1-D-Kinematics/Graphs-and-Ramps

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