Usually average speed means the rationof total distace travelled to the total time elapsed. However, sometimes thephrase ` average speed can be the magnitude of the average velocity. Are the two same ? Discuss.

Explanation

No, usually they different meanings, as according to I-definition `v_(av) =`[distance/time]. Now as distance `ge` to II-definition `v_(av)=` [|displacement|/time]. Now as distance `ge` |displacement|, `v_(av) ge |vec(v)_(av)|`, i.e, usually average speed is greater than magnitude of average velocity, e.g., if a body returns to its starting point after some motion, then as distance travelled is finite while displacement is zero, so `v_(av) gt 0` but `|vec(v)_(av)| = 0`. However, in case of motion along a straight line without change in direction as |displacement| = distance, the two definitions will means same.