Relativistic speed of a particle

[harpf]

Homework Statement

Find the speed of a particle whose total energy is twice its rest energy.

Homework Equations

E² = p²c² +m²c⁴

The Attempt at a Solution

4m²c⁴ = p²c² +m²c⁴
3m²c⁴ = p²c²
SQRT(3)mc² = pc
SQRT(3)mc = p
SQRT(3)mc = mv
SQRT(3)c = v
I know I can use E = gamma*mc² to get the answer, but what have I done wrong in my approach? Thank you.

 

[Doc Al]

SQRT(3)mc = p
SQRT(3)mc = mv

Your mistake was thinking that momentum equals mv. That's not true in relativity. In relativity, p = gamma*mv.

 

[harpf]

Thank you. I appreciate the help.