I remember just how hard it was for me to develop intuition for the idea of momentum in school. I hated that it seemed like an arbitrary multiplication p=m*v with no physical justification.
Eventually I acquired a (math, not physics) taste for it as a reified conserved quantity
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It is weird to imagine now, but back in Leibniz’ time, before Newton’s laws had become second nature, “motion” was as mysterious as “time” today.
17th c writing on motion seems just weirdly baroque/fussy. Here’s a sort of vitalist view of kinetic energy
plato.stanford.edu/entries/spacet

