I just started CM (I had 2 classes until now) and the professor said that if you know the position and velocity of say all the particles, then you know how the system will evolve. This, I already read and knew. I've probably a common question so feel free to redirect me to any similar thread. Here it comes: Suppose you're given the position and velocity of 2 particles. They are making contact and their velocity is 0 m/s. How do you know if a moment later they will start to move away from each other because they had a collision or if they will stay motionless, i.e. will remain stuck together? (Suppose the universe is constituted by these only 2 particles) If I knew v(t) it would be a different story, but only knowing v at a certain moment makes me wonder. Maybe it's like having a second order differential equation (representing the motion of each particles) that is totally unknown, but you have y'(0) and y(0). But I'm not sure at all on this. Could you answer my first question in words? Or maybe mathematically? Thanks for any help.