Kinetic Energy

Kinetic energy is the energy something has purely because it’s moving. It shows up everywhere in this topic — every time work is done to speed something up, that energy has to end up somewhere, and this is where it goes.

What Is Kinetic Energy?

Kinetic energy is the energy an object possesses because it’s in motion — the faster it moves, the more kinetic energy it carries. An object that’s speeding up is gaining kinetic energy, usually because another energy store (like gravitational potential energy, or the chemical energy in fuel) is being transferred into it via work done.

Where E_k is kinetic energy in joules, m is mass in kilograms, and v is speed in m s⁻¹.

Kinetic Energy in Terms of Momentum

Mass and speed also determine an object’s momentum, so kinetic energy can be rewritten using momentum instead of speed. This version is especially handy in particle physics, where momentum is often the quantity you’re given.

Where p is momentum in kg m s⁻¹. Since p = mv, substituting this in and simplifying brings you straight back to ½mv² — the two equations describe exactly the same quantity, just written for different situations.

Why Speed Matters So Much

Because speed is squared in the kinetic energy equation, small changes in speed cause much bigger changes in energy. Doubling an object’s speed doesn’t double its kinetic energy — it multiplies it by four. Tripling the speed multiplies the kinetic energy by nine. Mass, by contrast, scales kinetic energy directly: doubling the mass simply doubles the kinetic energy.