Prove the general relationship between average speed and average velocity for motion along a straight line.
(a) Starting from the definitions of average speed and average velocity for a time interval Δt, express each quantity in symbolic form.
(b) Using only the fact that the total distance travelled in any journey is greater than or equal to the magnitude of the net displacement, establish the inequality vavg≥∣vˉ∣.
(c) State precisely the condition under which equality holds, and illustrate this special case with one concrete example described in words.