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I have a conceptual problem with this. I can conceive of a situation wheresecond
there are many identifiable forces (tension, gravity, wind resistance)
acting on an object, but a point mass has only one acceleration - the
derivative of its position - and it has only one position. There are
certainly accelerations it might have had if each of the forces acted
individually - but they don't.
I think it's simply bad pedagogy to set up a net acceleration that is
defined as a sum of a collection of phantom accelerations