# How do you solve d=\frac{1}{2}at^2?

How do you solve $$\displaystyle{d}={\frac{{{1}}}{{{2}}}}{a}{t}^{{2}}$$?

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Troy Lesure
Given equation can be solved for two remaining variables as follows
Solve for acceleration:
$$\displaystyle{2}{d}={a}{t}^{{2}}$$, divide by $$\displaystyle{t}^{{2}}$$
$$\displaystyle{a}={\frac{{{2}{d}}}{{{t}^{{2}}}}}$$
Solve for time:
$$\displaystyle{2}{d}={a}{t}^{{2}}$$, divide by a
$$\displaystyle{t}^{{2}}={\frac{{{2}{d}}}{{{a}}}}$$, take square of both sides
$$\displaystyle{t}=\sqrt{{{\frac{{{2}{d}}}{{{a}}}}}}$$
Units for acceleration are $$\displaystyle{\frac{{\text{meters}}}{{\text{second squared}}}}$$