According to the theory of relativity, the energy, E, of a body of mass m is given as a function of its speed, v, by $E=m c^{2}\left(\frac{1}{\sqrt{1-v^{2} / c^{2}}}-1\right)$ , where c is a constant, the speed of light.Assuming v

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According to the theory of relativity, the energy, E, of a body of mass m is given as a function of its speed, v, by $E=m c^{2}\left(\frac{1}{\sqrt{1-v^{2} / c^{2}}}-1\right)$ , where c is a constant, the speed of light.Assuming v < c, expand E as a series in v/c, as far as the second non-zero term.If v = 0.05c, approximate E using your expansion.Also, approximate E by the formula $E=\frac{1}{2} m v^{2}$ .By what percentage do your two approximations differ?

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The Answer of According to the theory of relativity, the energy, E, of a body of mass m is given as a function of its speed, v, by $E=m c^{2}\left(\frac{1}{\sqrt{1-v^{2} / c^{2}}}-1\right)$ , where c is a constant, the speed of light.Assuming v < c, expand E as a series in v/c, as far as the second non-zero term.If v = 0.05c, approximate E using your expansion.Also, approximate E by the formula $E=\frac{1}{2} m v^{2}$ .By what percentage do your two approximations differ?

According to the Theory of Relativity, the Energy, E, of a Body