[tex] \sf E_{cin} = \frac{m_{0} {v}^{2} }{2} = \frac{m_{0} {c}^{2} }{2} \: \cdot \frac{ {v}^{2} }{ {c}^{2} } \Rightarrow \\ \Rightarrow \: \sf \: E_{cin} = \frac{E_{0}}{2} \cdot \frac{ {v}^{2} }{ {c}^{2} } \Rightarrow \\ \Rightarrow \: \sf {v}^{2} = \frac{2E_{cin}}{E_{0}} \cdot {c}^{2} \Rightarrow \\ \Rightarrow \: \red{\boxed{\sf v = \sqrt{ 2\frac{E_{cin}}{E_{0}} \cdot c }}}[/tex]
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[tex] \sf E_{cin} = \frac{m_{0} {v}^{2} }{2} = \frac{m_{0} {c}^{2} }{2} \: \cdot \frac{ {v}^{2} }{ {c}^{2} } \Rightarrow \\ \Rightarrow \: \sf \: E_{cin} = \frac{E_{0}}{2} \cdot \frac{ {v}^{2} }{ {c}^{2} } \Rightarrow \\ \Rightarrow \: \sf {v}^{2} = \frac{2E_{cin}}{E_{0}} \cdot {c}^{2} \Rightarrow \\ \Rightarrow \: \red{\boxed{\sf v = \sqrt{ 2\frac{E_{cin}}{E_{0}} \cdot c }}}[/tex]