Why F = m * a? vs Why not F = m + a?

[optics.tech]

Why F = m * a?

Why not F = m + a?

 

[Integral]

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.

 

[HallsofIvy]

Of course, it would be (mathematically) possible to have something like $F= C_1mz+ C_2a$ where $C_1$ and $C_2$ are constants with the correct units ($C_1$ would have to have units of "Newtons per kg" or "meters per second squared" and $C_2$ 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".

 

[huntoon]

From: http://en.wikipedia.org/wiki/Newton's_laws_of_motion

"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."