Key Concepts: Work-Energy Theorem

The Work-Energy Theorem

The net work done on an object equals the change in its kinetic energy:

W_net = ΔKE = ½mv² − ½mu²

• If net work is positive → object speeds up (KE increases).
• If net work is negative → object slows down (KE decreases).
• If net work is zero → speed doesn't change.

Relationship to Newton's Second Law

• The theorem follows directly from F = ma and kinematics (v² = u² + 2as).
• W_net = Fd = mad = m(v² − u²)/2 = ΔKE.

Applications

• Finding braking distance: KE → 0 through friction. W_friction = ΔKE → μmgd = ½mv² → d = v²/(2μg).
• Determining how much work a variable force does over a distance (area under F-x curve).