published by
the Physics Education Technology Project

This outstanding simulation from the University of Colorado lets you move an object on the screen and see the resulting graphs of position, velocity, and acceleration. Alternatively, you can set the values of these three quantities and watch the corresponding motion (and listen to the sound effects). Also, you can view the velocity and acceleration vectors, so you can see them change. Try it!!

Please note that this resource requires
at least version 1.4, Java WebStart of
Java.

Author: Jennifer Broekman
Posted: January 20, 2008 at 2:26PM
Source: The Physics Front collection

It's very difficult to create a smooth position-time graph, so the acceleration-time graph is wild. Consequently, the acceleration vector becomes a distractor, rather than effectively illustrating what acceleration does.

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships

6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

9-12: 9B/H1b. Sometimes the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting).

9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

11. Common Themes

11B. Models

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

Expressions and Equations (6-8)

Represent and analyze quantitative relationships between
dependent and independent variables. (6)

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Functions (8)

Define, evaluate, and compare functions. (8)

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Use functions to model relationships between quantities. (8)

8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

High School — Functions (9-12)

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

F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

The Moving Man, one of the Physics Education Technology (PHET) simulations developed at the University of Colorado at Boulder, is an outstanding resource for learning kinematics. The user moves the image of a man back and forth in one dimension with the mouse, and the simulation plots the position, velocity, and acceleration, each in a different color, for twenty seconds. The user can run the simulation again in slow motion, and, a moving vertical bar sweeps along the graphs, showing the time.

But the resulting graphs are pretty ragged, so the user can opt to set the initial velocity and acceleration. In this case the graphs are the familiar straight lines and parabolas of kinematics--just what is needed to help give meaning to the equations.

Moreover, the user can add arrows for velocity and acceleration. The arrows are particularly valuable because they are clearly visible when looking at the man, so they provide information in real time.

PhET Simulation: The Moving Man. (2005, March 22). Retrieved July 5, 2015, from Physics Education Technology Project: http://phet.colorado.edu/en/simulation/moving-man

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