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 – v
2/c
2]
1/2So in your
case KE/E = 3 and so:
3 =
g – 1 or
g = 4
Therefore: 1/[1 –
v
2/c
2]
1/2 = 4 and [1 – v
2/c
2] =
1/16
This gives: v
2/c
2 = 15/16 and so v = 0.968c. The correct
answer is (d)