Equations and experiments in physics give mathematical concepts physical meaning. One example is the fundamental equation of dynamics, F→=mγ→\overrightarrow{F} = m \overrightarrow {\gamma}, which states that the resultant force F→\overrightarrow{F} acting on a body in an inertial frame is proportional to its acceleration γ→\overrightarrow {\gamma}. Acceleration, in turn, has the same dimensions as a second derivative, thereby giving the second derivative a physical meaning.
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On the rails… --------------------
Consider a passenger on a train. Assuming that the train travels at a constant speed, the basic requirement for passenger comfort is that travellers should not be subjected to excessive forces. Galileo, who used the example of a passenger aboard a boat, understood that uniform motion in a straight line presented no difficulty. Unfortunately, trains do not travel from point A to point B in a straight line all the way!
In the case of a train, the path is fixed by the rails, which are a priori continuous. The forces acting on passengers come from two sources: the train's propulsion and the curvature of the rails.