According to the theory of special relativity, the mass of a particle increases as its velocity approaches the speed of light. The relationship between the rest mass (m₀) of a particle and its relativistic mass (m) at a given velocity (v) can be expressed by the equation:
m = γ * m₀
where γ (gamma) is the Lorentz factor given by:
γ = 1 / sqrt(1 - (v²/c²))
In this equation, c represents the speed of light in a vacuum.
Given that the mass (m) of the particle is equal to four times its rest mass (m₀), we can write:
4 * m₀ = γ * m₀
Dividing both sides by m₀, we have:
4 = γ
Squaring both sides, we get:
16 = γ²
Solving for γ, we find:
γ = 4
Substituting this value back into the Lorentz factor equation, we have:
4 = 1 / sqrt(1 - (v²/c²))
Squaring both sides and rearranging the equation, we get:
1 - (v²/c²) = 1/16
(v²/c²) = 15/16
Taking the square root of both sides and simplifying, we find:
v/c = sqrt(15) / 4
Therefore, the particle is moving at a speed equal to (sqrt(15) / 4) times the speed of light (c).