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I mainly teach physics, only a little math on the side. If I was teaching this math topic and wanted to spend 3 minutes giving the appropriate physical motivation, I would do something like the following. There is something called energy. It comes in various forms. Food has energy, which is what we're talking about when we talk about calories. Heat, sound, ...


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The best way to illustrate the sense of $W=|F||AB|\cos(\alpha)$ is to show that it makes sense that each of the factors is proportional to the work done. If you double the amount of force to an object to move it a certain distance, it doubles the amount of work needed. If you double the distance to move an object by applying a certain force, it doubles the ...


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