👉 The physical math underlying motion and change is rooted in Newton's laws of motion and the principles of calculus. Newton's first law, inertia, states that an object at rest stays at rest and an object in motion continues moving with constant velocity unless acted upon by a net external force—a concept mathematically expressed through the equation F = ma (force equals mass times acceleration), where acceleration is the derivative of velocity with respect to time. Newton's second law extends this, linking force, mass, and acceleration via F = ma, while his third law (action-reaction) is inherently tied to vector mathematics. Calculus then provides the tools to describe continuous change: derivatives measure instantaneous velocity (rate of change of position) and acceleration (rate of change of velocity), while integrals compute displacement, area under curves, or total work done. These principles unify the mathematical description of motion, from Newtonian mechanics to relativistic and quantum frameworks, where spacetime curvature (Einstein’s general relativity) further complicates the relationship between mass, energy, and spacetime geometry.
