At what speed must an object be moving in order that it has a kinetic energy 1.50 times its rest energy? (c = 3.00 x 10⁸ m/s) A)1.91 x 10⁸ m/s B)2.52 x 10⁸ m/s C)2.75 x 10⁸ m/s D)2.90 x 10⁸ m/s

Question

Quizplus · Accepted Answer

The equation to calculate kinetic energy (K) is K = (γ - 1)mc^2, where γ = 1/√(1 - v^2/c^2) is the Lorentz factor and m is the rest mass of the object. 
We are given that K = 1.5mc^2, so we can use this information to solve for v. 
1.5mc^2 = (γ - 1)mc^2 
1.5 = γ - 1 
γ = 2.5 
Substituting γ into the expression for γ gives: 
2.5 = 1/√(1 - v^2/c^2) 
Squaring both sides and solving for v gives: 
v = c√(1 - 1/γ^2) = 2.75 x 10^8 m/s. Therefore, the answer is C).

At What Speed Must an Object Be Moving in Order