Mechanics

Kinetic energy - formula in LaTeX

The energy of translational motion. It grows with the square of the speed, so a body moving twice as fast carries four times as much. A one-letter subscript is written E_k; anything longer needs braces, E_{kin}, or only the first letter is lowered.

E_k = \tfrac{1}{2}m v^2

LaTeX code

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$$
E_k = \tfrac{1}{2}m v^2
$$

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What the symbols mean

$E_k$: kinetic energy (J)
$m$: mass (kg)
$v$: speed (m/s)

A classical mechanics formula - it shows up in kinematics and dynamics problems and in physics lab reports.

Worked example

A 4 kg medicine ball flies at 5 m/s. Put \cdot between the fraction and the number: without it \tfrac{1}{2}\,4 is easy to misread as a mixed number.

E_k = \tfrac{1}{2} \cdot 4\,\mathrm{kg} \cdot (5\,\mathrm{m/s})^2 = 50\,\mathrm{J}

LaTeX commands in this formula

x_{0}: subscript; wrap several characters in braces
\tfrac: small fraction, as in running text
x^{2}: superscript (power); wrap several characters in braces

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