- #1

prosteve037

- 110

- 3

After reading many different websites and sources, I think I've developed a pretty good handle on how [itex]\textit{F= ma}[/itex] was formed, why it's the way it is, and how it's an equation that is scientifically viable.

However, I'm at a loss when it comes to explaining how the MATHEMATICAL formulation can be proven from the ground up. I can get to explaining how [itex]\textit{a}[/itex][itex]\propto[/itex][itex]\frac{x}{m}[/itex] ([itex]\textit{x}[/itex] being the constant of proportionality), but I can't explain why "[itex]\textit{x}[/itex]" turns to "[itex]\textit{F}[/itex]". From my understanding, [itex]\textit{F = ma}[/itex] is merely the result of that proportionality statement which is backed up directly by experiment. But how does "[itex]\textit{F}[/itex]" take the place of "[itex]\textit{x}[/itex]"?

Is it merely because Force, "[itex]\textit{F}[/itex]", is the only variable left out of the equation? Or is there a mathematical reason behind it? If so, what are the steps that show how "[itex]\textit{x = F}[/itex]"?

Thanks!