What is the work-energy theorem?

• A. Work equals force times distance
• B. Work done on an object equals the change in its kinetic energy
• C. Power equals work divided by time
• D. Energy is conserved in mechanical systems

Answer: (B)

The work-energy theorem says that the work done on an object by all forces equals the change in its kinetic energy. In math terms, W_net = ΔK = (1/2) m v^2 − (1/2) m u^2, where u is the initial speed and v is the final speed. This means when forces act to speed up an object, the energy transferred as work becomes kinetic energy, and the amount of energy gained matches the work put in.

For a constant force along the motion, the work is W = F·d, but the deeper idea the theorem expresses is that this energy transfer shows up as a change in motion, not just a force-distance product. Power, the rate of doing work, is P = dW/dt, which connects how fast energy is transferring into kinetic energy. The other statements relate to useful related concepts (work as a specific case, and energy conservation as a broader principle or the notion of energy transfer rate), but they don’t state the direct relationship between work and the object’s kinetic energy the way the theorem does.