Here is the way; that hasn’t been changed in a long time. We, start with a simple object, and we note that, such an object is defined for its motion by whats called, its location in space = x, or, the increments in its location, which is called, an infinitesimal distance = dx, the instantaneous time at which its motion is referred, t, or, the increments in its time, called dt.
Thats it. And, we would like to know; all that the object does in terms of x, t.
I would not like it, if my dear people sit in a car, and it vanished into thin air and never came back. I would like to keep track of it, the car, because I know my people would still be in it. I would like to, keep track of satellites, and, missiles and airplanes, I would like to know, whats happening around me, and why its happening.
It all started, with the quest, to solve for the trajectory, and then, became more complicated, as the complexity of these objects or systems grew. Collectively, they satisfy greatly, the quest we had set on, since the millennium and more, to understand, whats all, that goes on, in our universe, in our close vicinity, and in situations far off from us, as far as the extraneous bounds of the galaxy, in which we live, and more and more and more and deeper and deeper.
Then, x, t are not sufficient, to describe such situations. But, since its all systematic, we know all that has been defined, its not a party or Ramstein Music Band, where you forgot what happened yesterday. Its Hello Physics Inc. Pay Attention.
Now, as we defined dx and dt, we also note that, their ratio, or as-is-called, rate of x wrt t, called speed = v, is often formally written, as, x with a dot on it, … Its the first order time derivative of x = …
We also form, two quantities;
1. from v we form m.v = p = momenta, by multiplying the mass m into the velocity or speed v.
2. from a, we form in the same way, F = m.a = force.
But, force is also defined to be the time-rate of change of momentum p, or in other words, the ratio of the increments dp and dt, …
This latter is called Newton’s 2nd law; …
Its called a law, but strictly speaking, its a mathematical law so far, and not one which describes, universe’s phenomena so it cannot be called, a physical law or principle as of yet.
This point was originally raised by Feynman; as far as I know.