F the total energy of a particle is exactly thrice its rest energy, the velocity of the particle is:
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E = mc^2 / sqrt(1-v^2/c^2)
Because E is given to be 3mc^2, we have
sqrt(1-v^2/c^2) = 1/3
1-v^2/c^2 = 1/9
v^2/c^2 = 8/9
v/c = sqrt(8/9) = sqrt(8)/3 = 2sqrt(2)/3
v = 2sqrt(2) c / 3
Because E is given to be 3mc^2, we have
sqrt(1-v^2/c^2) = 1/3
1-v^2/c^2 = 1/9
v^2/c^2 = 8/9
v/c = sqrt(8/9) = sqrt(8)/3 = 2sqrt(2)/3
v = 2sqrt(2) c / 3
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