Relativistic motion under a constant force from rest
= Relativistic motion under a constant force from rest
Under a constant force $F$ with $p(0)=0$, momentum is $p=Ft$ and
$$
v(t)=\frac{Ft/m}{\sqrt{1+|F|^2t^2/(m^2c^2)}}.
$$
The speed approaches $c$ without reaching it at finite time.