# Calculate the speed, total and kinematic energy of a proton at the moment when its mass is equal

Calculate the speed, total and kinematic energy of a proton at the moment when its mass is equal to the rest mass of an α-particle.

Body mass at relativistic speeds is determined by the formula:
m = m0 / √ (1-v ^ 2 / c ^ 2) where m is the mass of the body, m0 is the rest mass v is the speed c is the speed of light.
So the mass of an α-particle is equal to four masses of a proton, we get:
4 * mo = m0 / √ (1-v ^ 2 / c ^ 2)
√ (1-v ^ 2 / c ^ 2) = 1/4
(1-v ^ 2 / c ^ 2) = 1/16
v ^ 2 / c ^ 2 = 15/16
v = √15 / 4 * c
Kinetic energy is determined by the formula:
E = mc ^ 2 / √ (1-v ^ 2 / c ^ 2) -mc ^ 2. where m is the proton mass, v is the velocity found above.

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