More generally, assuming that frame S′ is moving at velocity v with respect to frame S, then within frame S′, observer O′ measures an object moving with velocity u ′. Velocity u with respect to frame S, since x = ut, x ′ = x − vt, and t = t ′, can be written as x ′ = ut − vt = (u − v) t = (u − v) t ′. This leads to u ′ = x ′ / t ′ and ultimately