To recover the previous expressions for relative velocity, we assume that particle A is following the path defined by dx/dt in the unprimed reference (and hence dx ′/ dt ′ in the primed frame). Thus d x / d t = v A ∣ ∣ O and d x ′ / d t = v A ∣ ∣ O ′ , where O and O ′ refer to motion of A as seen by an observer in the unprimed and primed frame, respectively. Recall that v is the motion of a stationary object in the primed frame, as seen from the unprimed frame. Thus we have v = v O ′ ∣ ∣ O , and: