B How to derive the 4 laws of motion using Calculus

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The laws of motion cannot be derived purely from calculus, as they are fundamentally physical laws based on empirical observation and experimentation. While calculus can be used to express and develop these laws mathematically, their origins lie in physical principles rather than mathematical foundations. The formulation of these laws requires postulation based on real-world phenomena. Therefore, understanding the laws of motion involves both mathematical representation and physical experimentation. Ultimately, the relationship between calculus and the laws of motion is one of application rather than derivation.
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How do you derive the laws of motion using Calculus from scratch
 
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You can't. The laws of motion are physical laws, independent of the foundations of mathematics. The laws can be stated in mathematical form and developed using mathematics, such as calculus.

But, they have to be postulated through observation and experiment.
 
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
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