At what speed must an object be moving in order that it has a kinetic energy 2.6 times its rest energy? (c = 3.00 × 10⁸ m/s) A)2.77 × 10⁸ m/s B)2.17 × 10⁸ m/s C)2.88 × 10⁸ m/s D)1.15 × 10⁸ m/s E)2.55 × 10⁸ m/s

Question

Quizplus · Accepted Answer

The kinetic energy (KE) of an object is given by:

KE = (γ - 1)mc^2

where γ is the Lorentz factor, m is the rest mass of the object, and c is the speed of light.

We are given that the KE is 2.6 times the rest energy, so:

KE = 2.6mc^2

Substituting this into the first equation and simplifying, we get:

γmc^2 = 2.6mc^2 + mc^2

γ = 3.6

Now, the Lorentz factor is given by:

γ = 1/√(1 - v^2/c^2)

where v is the speed of the object.

Substituting γ = 3.6 and c = 3.00 × 10^8 m/s into this equation, we get:

3.6 = 1/√(1 - v^2/(3.00 × 10^8)^2)

Solving for v, we get:

v = 2.88 × 10^8 m/s

Therefore, the answer is choice C, 2.88 × 10^8 m/s.

At What Speed Must an Object Be Moving in Order