Løs varepsilon_{c}=1/2mv^2

$$\varepsilon _ { c } = \frac { 1 } { 2 } m v ^ { 2 }$$

Løs for m (complex solution)

$$\left\{\begin{matrix}m=\frac{2\epsilon _{c}}{v^{2}}\text{, }&v\neq 0\\m\in \mathrm{C}\text{, }&\epsilon _{c}=0\text{ and }v=0\end{matrix}\right,$$

Vejledning i at løse lineær ligning

Skift side, så alle variable led er placeret på venstre side.

$$\frac{1}{2}mv^{2}=\epsilon _{c}$$

Ligningen er nu i standardform.

$$\frac{v^{2}}{2}m=\epsilon _{c}$$

Divider begge sider med \frac{1}{2}v^{2}.

$$\frac{2\times \frac{v^{2}}{2}m}{v^{2}}=\frac{2\epsilon _{c}}{v^{2}}$$

Division med \frac{1}{2}v^{2} annullerer multiplikationen med \frac{1}{2}v^{2}.

$$m=\frac{2\epsilon _{c}}{v^{2}}$$

Løs for m

$$\left\{\begin{matrix}m=\frac{2\epsilon _{c}}{v^{2}}\text{, }&v\neq 0\\m\in \mathrm{R}\text{, }&\epsilon _{c}=0\text{ and }v=0\end{matrix}\right,$$

Vejledning i at løse lineær ligning

Skift side, så alle variable led er placeret på venstre side.

$$\frac{1}{2}mv^{2}=\epsilon _{c}$$

Ligningen er nu i standardform.

$$\frac{v^{2}}{2}m=\epsilon _{c}$$

Divider begge sider med \frac{1}{2}v^{2}.

$$\frac{2\times \frac{v^{2}}{2}m}{v^{2}}=\frac{2\epsilon _{c}}{v^{2}}$$

Division med \frac{1}{2}v^{2} annullerer multiplikationen med \frac{1}{2}v^{2}.

$$m=\frac{2\epsilon _{c}}{v^{2}}$$

Løs for v (complex solution)

$$\left\{\begin{matrix}v=-m^{-\frac{1}{2}}\sqrt{2\epsilon _{c}}\text{; }v=m^{-\frac{1}{2}}\sqrt{2\epsilon _{c}}\text{, }&m\neq 0\\v\in \mathrm{C}\text{, }&\epsilon _{c}=0\text{ and }m=0\end{matrix}\right,$$

Løs for v

$$\left\{\begin{matrix}v=\sqrt{\frac{2\epsilon _{c}}{m}}\text{; }v=-\sqrt{\frac{2\epsilon _{c}}{m}}\text{, }&\left(\epsilon _{c}\geq 0\text{ and }m>0\right)\text{ or }\left(\epsilon _{c}\leq 0\text{ and }m<0\right)\\v\in \mathrm{R}\text{, }&\epsilon _{c}=0\text{ and }m=0\end{matrix}\right,$$