If the velocity of a nonrelativistic object is doubled, its energy is quadrupled. This is only true for velocities that are very small compared with the speed of light. At what velocity would a doubling of velocity result in a doubling of energy?
A) 0.45c
B) 0.33c
C) 0.11c
D) 0.20c
E) 0.50c

Question

Quizplus · Accepted Answer

For relativistic speeds, the kinetic energy (KE) of an object is given by the equation $ KE = (\gamma - 1)mc^2 $, where $ \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} $ is the Lorentz factor, $ m $ is the mass of the object, and $ c $ is the speed of light. Doubling the energy in the relativistic regime does not simply result from doubling the velocity, as it would in classical mechanics due to the non-linear relationship introduced by the Lorentz factor. At a velocity of 0.45c, the increase in kinetic energy due to the relativistic effects is such that doubling the velocity approximately doubles the energy, rather than quadrupling it as would be predicted by non-relativistic physics. This makes choice A the correct answer, as it represents a scenario where relativistic effects significantly alter the relationship between velocity and kinetic energy.

If the Velocity of a Nonrelativistic Object Is Doubled, Its