If the rocket's speed doubles while mass stays the same, by what factor does its kinetic energy increase?

If the rocket's speed doubles while mass stays the same, by what factor does its kinetic energy increase?

• A. Doubles
• B. Triples
• C. Quadruples
• D. Halves

Answer: (C)

Kinetic energy depends on the square of speed, KE = 1/2 m v^2. If the speed doubles while mass stays the same, the new energy is 1/2 m (2v)^2 = 1/2 m · 4v^2 = 4 · (1/2 m v^2). So the kinetic energy increases by a factor of four. This squared relationship means small changes in speed produce larger changes in energy. Doubling speed does not simply double or triplicate energy—it quadruples it.

Kinetic energy depends on the square of speed, KE = 1/2 m v^2. If the speed doubles while mass stays the same, the new energy is 1/2 m (2v)^2 = 1/2 m · 4v^2 = 4 · (1/2 m v^2). So the kinetic energy increases by a factor of four. This squared relationship means small changes in speed produce larger changes in energy. Doubling speed does not simply double or triplicate energy—it quadruples it.