# S=vt in special relativity

1. Apr 1, 2012

### athrun200

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Can I do it like this:
$F=γma$
$F=γm\frac{dv}{dt}$
$F=γm\frac{dv}{ds}\frac{ds}{dt}$
$v\frac{dv}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{F ds}{m}$

v=$\frac{\sqrt{2c^2mFx-Fx}}{mc}$

What's wrong?

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Last edited: Apr 1, 2012
2. Apr 1, 2012

### K^2

$$F=\frac{dp}{dt}$$
$$F=\frac{d}{dt}(\gamma mv)$$
$$F=\gamma m \frac{dv}{dt} + mv\frac{d\gamma}{dt}$$

Because gamma is a function of v and varies with time, you run into problems. You should still be able to solve it this way if you take the extra term into account, but it's a lot more work than energy conservation method.