How Fast is an Object When Its Mass Triples?

[DB]

What is the speed of an objects whose mass is three times its rest mass.

I had some trouble with this question, but I would like to know if for these type of questions, is it safe to say that the velocity of a particle/object is equal to:

$$v=\sqrt{\mid\frac{{m_0}^2}{{X_{m_0}}^2}-1\mid c^2$$

Where $$X$$ is equal to how many times larger it's relativistic mass is compared to it's rest mass.

? just curious...

PS: \mid represents absolute value, but I think it would also work if:

$$v=\sqrt {-(\frac{{m_0}^2}{{X_{m_0}}^2}-1)c^2}$$

 

[vincentchan]

you do not have a relativity problem, you have an algebra problem... check your algebra

m=m_0 / sqrt (1-(v/c)^2)
v=sqrt(1-(m_o/m)^2)c

 

[wais]

Yes, your formula is correct for calculating the velocity of an object with a relativistic mass that is X times larger than its rest mass. The absolute value is necessary because the square root cannot take a negative value. So for an object with a relativistic mass that is three times its rest mass, the velocity would be:

v=\sqrt{\mid\frac{{m_0}^2}{{3{m_0}}^2}-1\mid c^2} = \sqrt{\mid\frac{1}{9}-1\mid c^2} = \sqrt{\mid-\frac{8}{9}\mid c^2} = \frac{2}{3}c

So the speed of the object would be two-thirds the speed of light.