A Novel Analytical Formulation for Deriving Net Force Directly from Instantaneous Displacement Equations

Abstract

Observations in classical mechanics education reveal that students frequently face challenges when deducing the net force Fnet from the instantaneous displacement equation (r (t)). The conventional approach, rooted in Newton's Second Law (F net= ma ), necessitates a series of sequential differentiations which can be prone to error. To streamline these derivations and provide a more direct analytical tool for dynamic analysis, this paper introduces a derived formula that allows for the straightforward determination of net force directly from displacement. This work facilitates a more efficient connection between kinematic descriptions and their underlying dynamic causes, offering both pedagogical benefits and analytical precision.