A car travels a total distance L. It travels half the distance with speed v₁ and the other half with speed v₂. The average speed of the car is:

A) (v₁ + v₂) / 2
B) 2v₁v₂ / (v₁ + v₂)
C) (v₁ + v₂)L / 2v₁v₂
D) 0

Average speed is defined as the total distance covered divided by the total time taken [1]. For a total distance L, the car travels the first half (L/2) at speed v1 and the second half (L/2) at speed v2. The time taken for the first segment is t1 = (L/2)/v1 = L/(2v1), and for the second segment is t2 = (L/2)/v2 = L/(2v2). The total time is the sum of these intervals: t = L/(2v1) + L/(2v2) = L(v1 + v2) / (2v1v2). Dividing the total distance L by this total time yields the average speed: L / [L(v1 + v2) / (2v1v2)] = 2v1v2 / (v1 + v2). This result is the harmonic mean of the two speeds, which is the standard formula for average speed when equal distances are covered at different rates [2].

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > 8.3 Speed > p. 113
2. [2] http://www.ma.huji.ac.il/~zamir/papers/55_Average%20Speed%20Bumps.pdf