Inequalities Applied to Kinematic Quantities

Abstract

SummaryIt is known that velocity averaged over time is less than or equal to velocity averaged over distance. This inequality is illustrated with some routine applied mathematics problems involving simple harmonic motion and free fall motion. Generalizations to motion along space curves are explored, and inequalities involving spatial and temporal averages of other kinematic/dynamic quantities are derived from Chebyshev’s sum inequality. These quantities include kinetic energy, tangential and normal components of acceleration, work, and impulse.