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Kinetic energy and rest energy

QUESTION: At what speed is a particle travelling if its kinetic energy is three times its rest energy?

Possible choices:
(a) 0.879c
(b) 0.918c
(c) 0.943c
(d) 0.968c
(e) 0.989c

Answer:

The equation relating kinetic energy (KE) to rest energy (E) is:

KE = (g– 1)E where g = 1/[1 – v2/c2]1/2

So in your case KE/E = 3 and so:

3 = g – 1 or g = 4

Therefore: 1/[1 – v2/c2]1/2 = 4 and [1 – v2/c2] = 1/16

This gives: v2/c2 = 15/16 and so v = 0.968c. The correct answer is (d)
 
 
 
© Keith Gibbs 2007