What is the equation for kinetic energy?

• A. KE = m v
• B. KE = 1/2 m a^2
• C. KE = m g h
• D. KE = 1/2 m v^2

Answer: (D)

Kinetic energy is the energy an object has because it is moving, and it depends on both how heavy it is and how fast it travels. The formula shows that energy of motion equals one-half times the mass times the velocity squared. The one-half factor and the velocity squared aren’t arbitrary: they come from how much work is required to accelerate an object from rest. Because velocity is squared, speed has a big effect on energy—doubling the speed makes the energy increase by a factor of four, while doubling the mass doubles the energy.

Check the units to see it makes sense: kilograms times (meters per second) squared gives kilograms times square meters per second squared, which is joules, the standard unit of energy.

The other expressions don’t match kinetic energy: momentum is m v, not energy; potential energy from gravity is m g h; and combining mass with acceleration (1/2 m a^2) mixes variables that describe motion differently and doesn’t represent the energy of motion.