{\large \begin{array}{l}E\,=\,\int{F\,ds\,\,}\xrightarrow{F\,=\,konst.}\,E\,=\,F\,\cdot \,s\\\\ E\,=\,\,\,\,\,\, \textcolor{blue}{F}\,\,\,\,\cdot \,\,\,\,\,\,\,\, \textcolor{red}{s}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \textcolor{blue}{F\,=\,m\,\cdot \,a}\\\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \textcolor{red}{s\,=\,\frac{1}{2}\,\cdot \,a\,\cdot \,{{t}^{2}}}\\\\E\,=\, \textcolor{blue}{m\,\,\cdot \,\,a}\,\,\,\cdot \,\,\,\ \textcolor{red} {\frac{1}{2}\,\cdot \,a\,\cdot \,{{t}^{2}}}\,\,\,\,\,\,\,\,\,\,v\,=\,a\,\cdot \,t\,\Rightarrow \, \textcolor{green}{t\,=\,\frac{v}{a}}\\\\E\,=\,m\,\,\cdot \,\,a\,\,\,\cdot \,\,\frac{1}{2}\,\cdot \,a\,\cdot \,\textcolor{green}{\frac{{{v}^{2}}}{{{a}^{2}}}}\\\\ E\,=\,\frac{1}{2}\,\cdot \,m\,\cdot \,{{v}^{2}}\end{array}}
Da wir hier die Bewegungsenergie bzw. die kinetische Energie Ekin hergeleitet haben, gilt:
{\huge {{E}_{kin}}=\frac{1}{2}m\cdot {{v}^{2}}}