How to derive the 4 laws of motion using Calculus?

[MrDarkness]

How do you derive the laws of motion using Calculus from scratch

 

[PeroK]

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.

 

[realJohn]

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.

 

[wrobel]

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.