the kinetic energy of a particle is 3 times its rest energy. What is the speed of the particle?

Question

a) 0.984c
b) 0.950c
c) 0.968c
d) 0.976c

Answer 1

The rest energy is m*c^2. The relativistic kinetic energy is given by m*c^2 / √[1-(v/c)^2] - m*c^2. This latter is 3 times the rest energy, or

m*c^2 / √[1-(v/c)^2] - m*c^2 = 3*m*c^2

1/√[1-(v/c)^2] = 4

1 = 4√[1-(v/c)^2]

1 = 16[1-(v/c)^2] = 16 - 16*(v/c)^2

15 = 16*(v/c)^2

(v/c) = √[15/16] = .968

Answer 2

relativistic KE is: KE = mc²(?–a million) ? = a million/?(a million–V²/c²) if KE is 9x this is relax skill (mc²) meaning ? = 10 10 = a million/?(a million–V²/c²) a million–V²/c² = a million/a hundred V²/c² = ninety 9/a hundred V/c = (0.ninety 9)² = 0.ninety 8 .