5. A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is

5. A car moves from X to Y with a uniform speed v_u and returns to Y with a uniform speed v_d. The average speed for this round trip is

(a) \(\sqrt{v_u v_d}\)

(b) \(\frac{v_d v_u}{v_d+v_u}\)

(c) \(\frac{v_{ul}+v_d}{2}\)

(d) \(\frac{2 v_d v_u}{v_d+v_u}\)

Answer :  (d) \(\frac{2 v_d v_u}{v_d+v_u}\)

Average speed \(= \frac{\text{Total distance}}{\text{Total time}}\)

\(= \frac{2d}{\frac{d}{v_u}+\frac{d}{v_d}}\)

\(= \frac{2d}{\frac{d(v_u+v_d)}{v_u v_d}}\)

\(= \frac{2v_u v_d}{v_u+v_d}\)