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This note develops Newtonian mechanics from concrete problems that might motivate it. The point is not to begin with familiar formulas and attach names to them afterward. The point is to ask what we want to predict, discover what information is missing, and introduce a definition only when it solves that problem.

The central example is a cart attached to a spring. From it, we will motivate position, velocity, acceleration, inertial mass, force, momentum, impulse, kinetic energy, and potential energy.

This note continues Rediscovering Mechanics and Energy from Questions, which introduced kinetic and potential energy using a cart attached to a spring. That construction leaves one main question:

Are kinetic and potential energy the only possible kinds of energy, or are they merely the parts that happened to be useful for that problem?

We will follow the same method as before: begin with a question, use the measured update rules to answer it, and introduce a new energy term only when the calculation requires one.