Question

An object has a total energy that is two times its rest energy. What is its speed? Give answer in c.

what equation do i use to solve this? step by step anyone?

Answer 1

total energy=sqrt{(m0 c^2)^2 +(pc)^2)
and that is equal to 2mo c^2

4(mo c^2)^2=(mo c^2)^2 + (pc)^2
or (pc)^2=3( mo c^2)^2

or momentum p^2=(mo c^2) 3
or momentum p= mo c sqrt3

now, a particle of velocity v, has a momentum of mo/(sqrt(1-(v/c)^2) * v
so mo v/(factor)= mo c sqrt 3
or v= c*sqrt3*(sqrt(1-(v/c)^2)

v^2=3c^2 (1-(v/c)^2)

v^2(1+3)=3c^2
v= 3/4 c

check all that.