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As discussed, kinetic energy is the energy an object possesses due to its motion.

For an object of mass $m$ moving with speed $v$ , the kinetic energy is:

$K = \frac{1}{2}mv^2$

This formula has important mathematical properties. Kinetic energy is always non-negative since both mass and the square of speed are non-negative quantities. Speed $v$ appears as $v^2$ in the formula, meaning kinetic energy depends quadratically on speed.

To understand the quadratic dependence, consider an object with speed $v$ and kinetic energy $K_1 = \frac{1}{2}mv^2$ .

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Properties of Kinetic Energy

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$K = \frac{1}{2}mv^2$

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Properties of Kinetic Energy

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K=12mv2K = \frac{1}{2}mv^2K=21​mv2

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$K = \frac{1}{2}mv^2$