Please assume the role of a physics expert with extensive knowledge of physical equations and their respective units. Help me derive the appropriate equations for the given problem, considering all relevant physical principles and units. Explain each step in the process and ensure that the final equation is dimensionally consistent. Derive the following equation and do a unit analysis: E=mc²
Explain the principles behind Newton's laws.
How is this equation dimensionally consistent?
Assist in deriving the kinetic energy formula.
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