• 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.

• 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.

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

• 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.

• 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.

• 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.

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

Maneuver a simulated man and watch simultaneous graphs of his position, velocity, and acceleration.  For beginning learners, the acceleration graph may be closed.  Try teaming this simulation with the great companion lessons by PhET teacher-fellows, found under "Lesson Plans" above. Highly versatile resource; adaptable to a broad spectrum of abilities/levels.

• Physical Sciences K-8 Graphing Unit
• Physics First Graphing Unit
• Conceptual Physics Graphing Unit
• Algebra-Based Physics Graphing Unit
• AP/Calculus-Based Physics Graphing Unit