MODELING MOTION AND RATES OF CHANGE: APPLICATIONS IN PHYSICS (KINEMATICS)

Abstract

Differential calculus serves as the indispensable mathematical language for describing and analyzing motion. This paper explores the fundamental role of derivatives in kinematics, the branch of physics concerned with the description of motion without reference to its cause. We rigorously define concepts such as instantaneous velocity and acceleration as derivatives of position and velocity, respectively. Through illustrative examples, including one-dimensional motion under constant acceleration, projectile motion, and an introduction to simple harmonic motion, we demonstrate how the theoretical framework of differential calculus provides a powerful and precise tool for understanding and predicting the dynamics of physical systems.