Specialioji reliatyvumo teorija: Skirtumas tarp puslapio versijų
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Eilutė 73:
:<math>E_k=mv^2-\int_{0}^{v} mvdv=mv^2-\int_{0}^{v}\frac{m_{0}v}{\sqrt{1-\frac{v^2}{c^2}}}dv=mv^2-\int_{0}^{v}\frac{m_{0}v}{\sqrt{1-\frac{v^2}{c^2}}}{d(1-\frac{v^2}{c^2})\over {-2v\over c^2}}=</math>
:<math>mv^2+\int_0^v\frac{m_0 c^2}{2\sqrt{1-\frac{v^2}{c^2}}}d(1-\frac{v^2}{c^2})=mv^2+\Big(m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}\Big)\Big|_0^v=mv^2+m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}-m_{0}c^2;</math>
:<math>E_k\approx mv^2+m_0 c^2(1-{1\over 2}\frac{v^2}{c^2})-m_{0}c^2=mv^2+m_0 c^2-{m_0 v^2\over 2}-m_{0}c^2=mv^2-{m_0 v^2\over 2}={mv^2\over 2}={m_0 v^2\over 2},</math> kai greitis <math>v</math> nerealitivinis (daug mažesnis nei šviesos greitis).
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