If the kinetic energy of a particle is equal to its rest energy then its speed must be:
A)0.25c
B)0.50c
C)0.87c
D)c
E)unknown unless its mass is given

Question

Quizplus · Accepted Answer

The kinetic energy (K) of a particle equals its rest energy (E₀) when the particle's speed is such that its total energy (E) is twice its rest energy. Mathematically, this condition is represented as E = 2E₀. Since the total energy E is given by E = γE₀, where γ is the Lorentz factor (γ = 1/√(1-v²/c²)), setting E = 2E₀ gives γ = 2. Solving 1/√(1-v²/c²) = 2 for v yields v = √(3)/2 c ≈ 0.87c.

If the Kinetic Energy of a Particle Is Equal to Its