Hello, thanks for that article. Yes, this is correct and the way to recover that velocity in terms of t is to use the equation (2) in the OP which gives you the functional form of $$\gamma (\tau)$$ and then solve $$dt/d\tau = \gamma (\tau)$$.
Thanks, now my problem is complete.
I'm doing some special relativity exercises. I have to find $$x(t), v(t)$$ of a charged particle left at rest in $t=0$ in an external constant uniform electric field $$\vec{E}=E_{0} \hat{i}$$, then with that velocity I should find the Liénard–Wiechert radiated power.
I will show you what I did...