The energy of an electron at speed v in special relativity theory is mc2(1−v2/c2) −1/2, where m is the electron mass, and c is the speed of light. The factor mc2 is called the rest mass energy (energy when v = 0). Find two terms of the series expansion of (1 − v2/c2) −1/2, and multiply by mc2 to get the energy at speed v. What is the second term in the energy series? (If v/c is very small, the rest of the series can be neglected; this is true for everyday speeds.)

The energy of an electron at speed v in special relativity theory is mc2(1−v2/c2) −1/2, where m is the electron mass, and c is the speed of light. The factor mc2 is called the rest mass energy (energy when v = 0). Find two terms of the series expansion of (1 − v2/c2) −1/2, and multiply by mc2 to get the energy at speed v. What is the second term in the energy series? (If v/c is very small, the rest of the series can be neglected; this is true for everyday speeds.)

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