The kinetic energy of moving water is proportional to which expression?

• A. Velocity squared only
• B. Mass times velocity
• C. Mass times velocity squared
• D. Mass squared times velocity

Answer: (C)

Kinetic energy reflects both how much stuff is moving and how fast it’s moving, with the well-known formula KE = (1/2) m v^2. The factor of v^2 means the energy grows with the square of speed, and the m in front means more mass means more energy. Because of that, KE is proportional to the product of mass and the square of velocity: m v^2.

This also clarifies why the other ideas don’t fit. Velocity alone ignores how much water is moving; momentum is m v, which is a different physical quantity. Mass times velocity squared captures the true energy content, and mass squared times velocity would imply an incorrect dependence on mass. In moving water, you can think of the total energy carried by the flow as proportional to the mass moving times the square of its speed, reinforcing why the correct expression is mass times velocity squared.