At what speed must an object be moving in order that it has a kinetic energy 2.50 times its rest energy? (c = 3.00 × 10⁸ m/s) A) 2.52 × 10⁸ m/s B) 1.91 × 10⁸ m/s C) 2.75 × 10⁸ m/s D) 2.87 × 10⁸ m/s

Question

Quizplus · Accepted Answer

The kinetic energy (KE) is given by KE = (γ - 1)mc², where γ is the Lorentz factor. For KE = 2.5mc², γ - 1 = 2.5, so γ = 3.5. Solving for v in γ = 1/√(1-v²/c²) gives v ≈ 2.87 × 10⁸ m/s.

At What Speed Must an Object Be Moving in Order