Which of the graphs best represents the kinetic energy *K* of an elementary particle as a function of its speed , where is the speed of light?

### Select an Answer

graph (A)

graph (B)

graph (C)

graph (D)

graph (E)

### View Correct Answer

The correct answer is graph (B). In classical mechanics, which is appropriate to apply at low speeds, the kinetic energy *K* of a particle is given as a function of its speed by , where *m* is the mass of the particle. So *K* must be zero when is zero. But according to special relativity, which must be applied when speeds are near the speed of light *c*, the speed of a particle can approach but never reach or exceed *c*. *K* continues to increase as the speed increases, but the curve can only get closer to the line at and cannot intersect it. Graph (B) is the only one that satisfies both criteria; that is, it is zero when is zero and it approaches asymptotically.