Average Speed And Average Velocity

As stated in NCERT Class 11, Chapter 3 (Motion in a Straight Line), average speed is the total path length divided by the total time taken, and it is generally not the arithmetic mean of two speeds when equal distances are covered. Let each half cover a distance d. Time for the first half is t1 = d/10 and for the second half is t2 = d/15. Total distance is 2d and total time is d/10 + d/15 = (3d + 2d)/30 = 5d/30 = d/6. Therefore average speed = 2d ÷ (d/6) = 12 m/s, which is the harmonic mean of the two speeds. The option 12.5 m/s is wrong because it is the simple arithmetic mean, valid only for equal time intervals, not equal distances. The value 13 m/s has no kinematic basis here and overestimates the result. The value 11.5 m/s underestimates and arises from an arithmetic slip. Plausibility check: the average must lie closer to the slower speed since more time is spent at 10 m/s, and 12 m/s indeed lies below the midpoint of 12.5 m/s, confirming the answer.