In physics, energy E carries dimensions of mass times length squared divided by

Question

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. (Use the following as necessary: m, v, and k for the constant of proportionality. Assume that the proportionality constant k includes any relevant coefficient.)
E = ?

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. (Note, however, that the first relationship is associated with energy of motion, and the second with energy of mass. Use the following as necessary: m and c.)
E = ? when k = 1 and v = c

Explanation / Answer

E = kmv^2 E= mc^2

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