If the two particles are moving at the same speed in a vacuum, then their kinetic energy will be the same. The kinetic energy of a particle is given by the equation:
KE = (1/2)mv^2
Where KE is the kinetic energy of the particle, m is its mass, and v is its speed.
In this case, the kinetic energy of the particle with mass m will be:
KE = (1/2)m*v^2
And the kinetic energy of the particle with mass 3m will be:
KE = (1/2)3mv^2 = (3/2)mv^2
Since the particles have the same kinetic energy, we can set the two equations equal to each other and solve for v:
(1/2)mv^2 = (3/2)mv^2
(1/2)*v^2 = (3/2)*v^2
1/2 = 3/2
This equation does not have a valid solution, which means that the two particles cannot be moving at the same speed in a vacuum if one has a mass of m and the other has a mass of 3m.
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