Multiple choice

A vehicle travels half the distance L with speed $v_1$ and the other half with speed $v_2,$ then its average speed is

  1. $\frac{v_1 + v_2}{2}$
  2. $\frac{2v_1 + v_2}{v_1 + v_2}$
  3. $\frac{2v_1v_2}{v_1 + v_2}$
  4. $\frac{L(v_1 + v_2)}{v_1v_2}$
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C Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 2L. Time = L/v1 + L/v2. Average speed = 2L / (L/v1 + L/v2) = 2v1v2 / (v1+v2).

AI explanation

Using the formula for average speed when equal distances are covered at different speeds, we calculate the harmonic mean of the two speeds. The total distance is L, and the total time taken is the sum of L/2 divided by v1 and L/2 divided by v2. The average speed is total distance divided by total time, written as L divided by (L/2v1 + L/2v2). Factoring out L/2 from the denominator yields L divided by (L/2 multiplied by (1/v1 + 1/v2)), which simplifies to 2v1v2 divided by (v1 + v2).

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