Abstract
<jats:p>This paper presents a rigorous theoretical examination of kinetic energy across classical and relativistic domains. While Newtonian mechanics model’s kinetic energy as a straightforward function of mass and velocity squared, special relativity introduces Lorentz transformations that account for mass-energy equivalence and velocity limits near the speed of light. Utilizing a binomial series expansion of the Lorentz factor, this study demonstrates that Newtonian kinetic energy represents a valid first-order approximation at low velocities. However, as velocity approaches the speed of light, the higher-order relativistic terms become dominant, creating a substantial divergence between classical predictions and physical reality. The findings highlight the boundaries of classical mechanics and reinforce the necessity of relativistic models in high-energy physics applications</jats:p>