Work Energy And Power

Concept: The Work-Energy Theorem establishes a direct relationship between force and motion. It states that the total work done by the net force on a particle equals the change in its kinetic energy. Mathematically, where, This theorem connects Newton’s Laws of Motion with energy principles.
Mathematical Proof: Consider a particle of mass moving under a constant force . From Newton’s Second Law: We know that acceleration can be written as: Using the chain rule: Since , we get: Substitute into : Rearranging: Integrating both sides between initial and final states: Left side represents total work done : Thus, the net work done on a particle is equal to the change in its kinetic energy.