Mechanics

Distance (uniformly accelerated motion) - formula in LaTeX

Gives the position of a body moving with constant acceleration. If it starts from rest at the origin, only the last term remains. The one half is typeset with \tfrac so it stays the height of the surrounding text; in a displayed equation \frac works just as well.

s = s_0 + v_0 t + \tfrac{1}{2}a t^2

LaTeX code

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$$
s = s_0 + v_0 t + \tfrac{1}{2}a t^2
$$

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What the symbols mean

$s$: position after time t (m)
$s_0$: initial position (m)
$v_0$: initial velocity (m/s)
$a$: acceleration (m/s²)
$t$: time (s)

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

Worked example

A cyclist passes the origin at 2 m/s and accelerates at 3 m/s² for 4 s, so s₀ = 0. Put the squared time in parentheses together with its unit, (4\,\mathrm{s})^2, because the seconds are squared too.

s = 2\,\mathrm{m/s} \cdot 4\,\mathrm{s} + \tfrac{1}{2} \cdot 3\,\mathrm{m/s^2} \cdot (4\,\mathrm{s})^2 = 8\,\mathrm{m} + 24\,\mathrm{m} = 32\,\mathrm{m}

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

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
Paste it into the CamteX editor, Overleaf or any LaTeX document.
Inside a sentence, use single $…$ instead of double.
The formula needs the amsmath package - CamteX templates include it in the preamble.

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