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Connections
Object Method
Kinematics, Newton's First and Second Laws of Motion
algebra-based math with uniform acceleration equations  
calculus-based math  
Impulse-Momentum Theorem
algebra-based math with uniform acceleration equations  
calculus-based math, one dimension  
Work-Energy Theorem
Objects are assumed to have no internal structure, although they almost always do. We can only employ the work-energy theorem when there is no significant change in the potential energy within the object.
System Method
Newton's Third Law of Motion
algebra-based math with uniform acceleration equations, two objects  
Law of Conservation of Momentum

The Field Model of Interactions
Potential energy can be stored in fields
Law Of Conservation of Energy
This system-based model allows us to account for potential energy stored in the system, and for work done by external forces to change either the kinetic energy or the potential energy or both.
The law of conservation of energy is arguably the most fundamental concept in science.