• For any pair of interacting objects, the force exerted by the first object on the second object is equal in strength to the force that the second object exerts on the first, but in the opposite direction (Newton's third law). (6-8)
• The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. (6-8)
• Newton's second law accurately predicts changes in the motion of macroscopic objects. (9-12)

• The gravitational force of Earth acting on an object near Earth's surface pulls that object toward the planet's center. (5)

• Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to describe, test, and predict more abstract phenomena and design systems. (6-8)
  • Develop and use a model to describe phenomena. (6-8)
• 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)

• 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)
  • Use mathematical representations of phenomena to describe explanations. (9-12)
  • Create or revise a simulation of a phenomenon, designed device, process, or system. (9-12)

• 3-5: 4F/E1bc. The greater the force is, the greater the change in motion will be. The more massive an object is, the less effect a given force will have.
• 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/H2. All motion is relative to whatever frame of reference is chosen, for there is no motionless frame from which to judge all motion.
• 9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.
• 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/H3. Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation.
• 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.
• 6-8: 11B/M5. The usefulness of a model depends on how closely its behavior matches key aspects of what is being modeled. The only way to determine the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.

Move objects of varying mass along a 1-D path and watch as the simulation displays graphs of position vs. time, velocity vs. time, and acceleration.  Applied force, friction, and gravitational constants can be varied in this interactive activity. Can be adapted for use in either middle or high school.

• Physical Sciences K-8 Applications of Newton's Laws Unit
• Physics First Applications of Newton's Laws Unit
• Conceptual Physics Applications of Newton's Laws Unit
• Algebra-Based Physics Applications of Newton's Laws Unit
• AP/Calculus-Based Physics Applications of Newton's Laws Unit