newtonian mechanics - Why force $F$ is $ma$ but not $md$ or $mv$? How can I observe and understand "force" in real life?

As a layman, i can calculate approx "displacement" just by observing the moving object. And accurately by using a simple "scale". Similarly, again, I can calculate angle from origin by using displacement in $x$ and $y$ dimensions. Similarly I can use a stopwatch and scale to understand velocity.

But when I read about force, first of all it confuses with the english word "force", we use in real life. To some extent I am sure, it has nothing to do with that. So exactly what is it in the real sense. How can a layman, see force as, just like he can see displacement or angle? Or force is just a quantity defined by physicists to simplify the combinations of $ma$, they might be facing every time. And thus came up with term "force" ( which is similar in spelling to english word in oxford dictionary). And lastly, why not force has just been called as something proportional to mass and it's displacement or velocity. Why something at the level of change of velocity has been used to define it.

Answer

Interestingly enough, Aristotle proposed that $\vec F=m\vec v$, for, by intuition, it is reasonable to assume that how hard something hits you depends upon how heavy something is, and how hard something is going. However, this is because of Newton's First Law, inertia, which is analogous to momentum ($\vec p=m\vec v$). Yet, mass does have to have some effect on it, for it is not the same to have a truck hit you than to have a bee hit you. Thus, we reach the conclusion that a push or pull (a force) must be affected by the mass, and some factor dependent upon the derivatives of displacement with respect to time. Yet, what makes something move is not the speed with which it is hit, as we have discussed, but the change in speed, that is to say, the acceleration. Hence, $\vec F=m\vec a$.

I understand this is not the most theoretical derivation of a formula, it is rather an intuitive one, and it is very poorly written, for I am writing it on my phone and cannot even use LaTex. So please, don't hesitate to ask if you have any other questions or want a more theoretical approach.

Hope it helped!