Proper acceleration for one-dimensional motion
= Proper acceleration for one-dimensional motion
{title2=$a=\gamma^3\dot u=\frac{d(\gamma u)}{dt}$}
For motion on a fixed axis, the signed spatial <four-acceleration> in the instantaneous rest <inertial frame> is $a=\gamma^3\dot u$. Its magnitude is the scalar <proper acceleration>. Constant signed $a$ from rest gives $\gamma u=at$ and the <hyperbolic motion> worldline $x=(c^2/a)(\sqrt{1+a^2t^2/c^2}-1)$.