What is the Speed of a Particle with Total Energy 3 Times its Rest Energy?

[Delzac]

Homework Statement

Find the speed of a particle whose total energy is 3 times its rest energy.

Homework Equations

$$KE = \gamma mc^2 - mc^2$$

The Attempt at a Solution

i let total energy = 3mc^2 and then :

$$\gamma mc^2 = KE + mc^2$$
$$3mc^2 = KE + mc^2$$
$$v = \frac{\sqrt{3}}{2} c$$

Is this correct? or should i let $$\gamma mc^2 = 3mc^2$$ and work it out immediately?

Any help will be appreciated.

 

[chanvincent]

$$3mc^2 = KE + mc^2$$ is correct, but I don't see how is this connected to $$v = \frac{\sqrt{3}}{2} c$$, So I can't point out which part you did it wrong...

or should i let $$\gamma mc^2 = 3mc^2$$ and work it out immediately?

yes

 

[Meir Achuz]

Use 1/sqrt{1-v^2/c^2}=3,and solve for v.

 

[Delzac]

yeah, got it thanks, English problem. bah. :P