Quote by Moataz
Also, my book says that this formula only works in inertial frames.
[tex]\Delta \tau = \int \sqrt[]{1v^2}dt ; v=speed[/tex]
Bu that does not make sense because v is in terms of t and it is supposed to change over time which means there must be acceleration!?

"Inertial frame" means the
observer is not accelerating. It doesn't mean that the
object being observed can't accelerate.