Why F = m * a?
Why not F = m + a?
Adding acceleration and mass is just like adding apples and oranges, it can't be done.
Look at the units involved and combine them in a manner which makes sense.
Of course, it would be (mathematically) possible to have something like [itex]F= C_1mz+ C_2a[/itex] where [itex]C_1[/itex] and [itex]C_2[/itex] are constants with the correct units ([itex]C_1[/itex] would have to have units of "Newtons per kg" or "meters per second squared" and [itex]C_2[/itex] has units of "Newtons-seconds square per meter" or "kilograms".
But the only good Physics explanation as to why a specific formula is true is "that is what the experimental evidence shows".
"Newton's original Latin reads:
Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.
This was translated quite closely in Motte's 1729 translation as:
Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd."
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