 Since the trajectories of bodies are curves in spacetime, the affine connection determines the rate of change from straightness at every point of every possible trajectory. The straight trajectories thus defined can be interpreted as the trajectories of bodies moving inertially (i.e., without forces), and the rate of change from straightness of any trajectory can be interpreted as the acceleration of a body following that trajectory. That is, Newton’s First Law can be given a geometric formulation as ‘bodies on which no net forces act follow straight lines in spacetime’; similarly, the Second Law can be formulated as ‘the rate of change from straightness of a body’s trajectory is equal to the forces acting on the body divided by its mass’. The significance of this geometry is that while acceleration is well-defined, velocity is not – in accordance with the empirical determinability of acceleration (generally though not universally) but not of velocity, according to Newtonian mechanics. Thus Galilean spacetime gives a very nice interpretation of the choice that nature makes when it decides that the laws of mechanics should be formulated in terms of accelerations not velocities. (In fact, there are complications here: in light of Newton’s Corollary VI mentioned above, one might wonder whether even Galilean spacetime is the appropriate spacetime structure for Newtonian mechanics. Saunders (2013), for example, argues that in fact only a yet more impoverished spacetime structure – ‘Newton-Huygens spacetime’ – is needed.)