High School 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.
 
First of all, I thought there were 3 Newton's laws of motion.

Second of all (ironically speaking), the Newton's 2nd law states that F = ma. We can say that a is equivalent to the derivative of velocity wrt time. The derivative, in this case, uses calculus.
 
I do not understand which 4 laws are supposed to derive but the work energy theorem is usually derived from the 2nd Newton; as well as the angular momentum theorem is also a theorem and it is derived.
 

Thread 'Mousetrap Car Energy efficiency'

For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...
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