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Kinetic energy review

Review the key concepts, equations, and skills for kinetic energy.  Understand how kinetic energy can't be negative but the change in kinetic energy can be negative.

Key terms

Term (symbol)Meaning
Kinetic energyEnergy from translational or rotational motion. SI units of joules (J).
Translational motionLinear motion of a rigid body. SI units of ms.
Translational kinetic energy (K)Energy due to linear motion of a rigid body. SI units of joules (J).


EquationSymbolsMeaning in words
K=12mv2K is translational kinetic energy, m is mass, and v is the magnitude of the velocity (or speed)Translational kinetic energy is directly proportional to mass and the square of the magnitude of velocity.
ΔK=12m(v2v02)ΔK is change in kinetic energy, and v and v0 are the magnitudes of the final and initial velocityChange in kinetic energy is the difference between the final and initial kinetic energy.

Common mistakes and misconceptions

  1. Kinetic energy can’t be negative, although the change in kinetic energy ΔK can be negative. Because mass can’t be negative and the square of speed gives a non-negative number, kinetic energy can’t be negative. Either something is moving and has positive kinetic energy, or it is not moving and has zero kinetic energy. If the final speed is less than the initial speed, then the final kinetic energy is less than the initial kinetic energy and ΔK is negative.
  2. Some people think doubling speed means doubling the energy. The kinetic energy is proportional to the square of the speed, so doubling the speed increases the kinetic energy by a factor of 4. However, doubling the speed does double the momentum, which we will cover in the next unit.

Learn more

For deeper explanations of kinetic energy, see our article on kinetic energy with worked example problems.
To check your understanding and work toward mastering these concepts, check out the exercise on using the kinetic energy equation.

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