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1) Derive relativistic kinetic energy starting from Newton's second law defined with a relativistic force

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1) Derive relativistic kinetic energy starting from Newton's second law defined with a relativistic force. Show all the steps, especially the integration by parts. (6 pts)

2) Using the result of the previous problem, derive classical kinetic energy for low speeds.

3) Plot the velocity (v/c) of an object versus kinetic energy for both classical and relativistic calculations. (4 pts)

4) Determine whether an object with mass can ever have the speed of light. Elaborate (2)