Kinetic energy calculation (Ek = 1/2 m v^2)

What you need to know

• A moving object stores energy in its kinetic store — the faster or heavier it is, the more energy it holds.
• The equation to use is Ek = 1/2 m v^2 — you must be able to recall and apply this.
• Speed is squared, so doubling speed quadruples kinetic energy; doubling mass only doubles it.
• Units matter: mass in kg, speed in m/s, kinetic energy in joules (J).

The big picture

Any moving object stores energy in its kinetic store. The amount depends on both its mass and its speed, but speed matters far more — double the speed and the energy quadruples, because speed is squared in the equation Ek = 1/2 m v^2. This relationship explains why braking distances shoot up at higher speeds and why a small, fast object can carry more energy than a large, slow one. Mastering this equation means being able to calculate, compare, and explain energy changes in real-world situations.

What gives an object kinetic energy?

Follow each stage to build the full picture before you touch the equation.

1. 1

   An object is set in motion

   When a force acts on an object and it starts to move, energy is transferred into its kinetic store. The object now 'has' kinetic energy simply because it is moving.

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2. 2

   Mass contributes proportionally

   A heavier object moving at the same speed as a lighter one has more kinetic energy. If you double the mass, you double the kinetic energy — it's a straight, proportional relationship.

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3. 3

   Speed contributes with a square relationship

   Speed has a much bigger effect than mass. If speed doubles, kinetic energy quadruples — because v is squared in the equation Ek = 1/2 m v^2. This is the most important relationship on the page.

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4. 4

   Calculate using Ek = 1/2 m v^2

   Substitute mass in kg and speed in m/s into the equation. Always square v first, then multiply by mass, then halve — following this order prevents the most common calculation error.

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5. 5

   Energy transfers when the object slows or stops

   When a moving object decelerates — due to braking, air resistance, or impact — its kinetic store empties. That energy moves into other stores (e.g. the thermal store of brakes). The total energy is always conserved.

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Kinetic energy calculator

A 1500 kg car is travelling at 25 m/s. Calculate its kinetic energy using Ek = 1/2 m v^2.

Taken directly from the exam-board specification.

Memory hook

Half a Massive Vehicle Squared — ½ × m × v² — picture a huge lorry cut in half, moving fast. The 'half' reminds you of the ½, the 'Massive' is mass, and the 'Vehicle Squared' is v².

Check yourself

Without looking: if a cyclist doubles their speed, what happens to their kinetic energy — and which part of the equation tells you that?