I'm trying to learn verlet integration. I don't understand it very well to be honest. What I am having problem with is at the very beginning of it. I am reading the following, since I can't find it any simpler: https://www.gamedev.net/tutorials/programming/math-and-physics/a-verlet-based-approach-for-2d-game-physics-r2714/
What I am trying to understand is how exactly is it that velocity is represented with position(now) - position(old). How does it equal the estimate of v(now)*timestep? How is this possible?
This might be a completely stupid question, because I completely failed physics back when I studied it. There might be something blatantly obvious about it, but I am looking for the mathematical proof behind it that I can understand with hopefully 'high school' maths.