In physics, energy E carries dimensions of mass times length squared, divided by time squared. Use dimensional analysis to derive a relationship for energy in terms of mass m and speed v, up to a constant of proportionality. Set the speed equal to c, the speed of light, and the constant of proportionality equal to 1 to get the most famous equation in physics.

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Energy: kg m²s⁻² Mass = kg velocity = m/s E = kmv²; putting k = 1, v = c E = mc²

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