User:Covada/Sandbox

This is my own subpage used as a Sandbox.

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Example 1
${\begin{aligned}t&={\dfrac {s}{v}}\qquad h={\dfrac {gt^{2}}{2}}\\2\cdot h&=gt^{2}\qquad {\frac {2\cdot h}{g}}=t^{2}\qquad t={\sqrt {\dfrac {2\cdot h}{g}}}\\{\dfrac {s}{v}}&={\sqrt {\dfrac {2\cdot h}{g}}}\\v&={\dfrac {s}{\sqrt {\dfrac {2\cdot h}{g}}}}\\v&=s\cdot {\sqrt {\dfrac {g}{2\cdot h}}}\qquad v=s\cdot {\sqrt {\dfrac {9,81}{2\cdot h}}}\end{aligned}}$

Example 2

${\begin{aligned}\tau =R\cdot C\\1-e^{-1}\end{aligned}}$

Example 3
$B=\mu _{0}{\dfrac {N\cdot I}{l}}$
Example 4

${\begin{aligned}E_{k}&={\dfrac {1}{2}}mv^{2}\qquad E_{opgeslagen}={\dfrac {1}{2}}CU^{2}\qquad v=s\cdot {\sqrt {\dfrac {g}{2\cdot h}}}\\\\\eta &={\dfrac {E_{k}={\dfrac {1}{2}}mv^{2}}{E_{opgeslagen}={\dfrac {1}{2}}CU^{2}}}\cdot 100\%\\\eta &={\dfrac {mv^{2}}{CU^{2}}}\cdot 100\%\\\eta &={\dfrac {m\cdot \left(s\cdot {\sqrt {\dfrac {g}{2\cdot h}}}\right)^{2}}{CU^{2}}}\cdot 100\%\\\eta &={\dfrac {m\cdot s^{2}\cdot {\dfrac {g}{2\cdot h}}}{CU^{2}}}\cdot 100\%\\\eta &={\dfrac {m\cdot g\cdot s^{2}}{2\cdot h\cdot CU^{2}}}\cdot 100\%\\\end{aligned}}$