• 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)

• Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth). (9-12)

• Models can be used to represent systems and their interactions. (6-8)
• When investigating or describing a system, the boundaries and initial conditions of the system need to be defined. (9-12)

• 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)

• 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: 11B/M1. Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.
• 9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

• A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

Students can have fun exploring projectile motion as they interactively fire objects of varying mass from a cannon.  Users may set initial velocity, angle, and air resistance.  This resource would be teamed well with the Physics Classroom student tutorial on projectile motion (below).

• Physical Sciences K-8 Motion in More Than One Dimension Unit
• Physics First Motion in More Than One Dimension Unit
• Conceptual Physics Motion in More Than One Dimension Unit
• Algebra-Based Physics Motion in More Than One Dimension Unit
• AP/Calculus-Based Physics Motion in More Than One Dimension Unit