I'd like to see an example of a formula describing the position of a rolling ball over time. It has been given one impuls at the start, after which air resistance and friction decelerates it (the ground is flat). At high speed the ball might be sliding, until it decelerates to some treshold speed when it starts to roll. The deceleration might behave quite different in those two modes, I guess. How should I formulate the balls position as a function of time based on those characteristics? I intend to observe the position of a rolling (sliding) ball at different times, and I want to formulate a function to fit with those observations in order to figure out where the ball has been at any given point in time. I thought it might make more sense to estimate the parameters of a model with some basis in real physics, rather than to fit any curve.