Question

If a person moving along a straight line covers the first half of the distance with velocity \( V_1 \) and the next half with velocity \( V_2 \), then the average velocity is:

• A. \( \frac{V_1 + V_2}{2} \)
• B. \( \frac{(V_1 + V_2)}{2 \sqrt{V_1 V_2}} \)
• C. \( \frac{2}{\frac{1}{V_1} + \frac{1}{V_2}} \)
• D. \( \frac{V_1 V_2}{V_1 + V_2} \)

Hint:

For average speed over equal distances, use harmonic mean: \( V_{\text{avg}} = \frac{2 V_1 V_2}{V_1 + V_2} \).

Answer 1

The Correct Option is C

For equal distances \( d \), time taken: \( t_1 = \frac{d}{V_1}, t_2 = \frac{d}{V_2} \)
Total distance = \( 2d \), Total time = \( \frac{d}{V_1} + \frac{d}{V_2} \)
\[ V_{\text{avg}} = \frac{2d}{\frac{d}{V_1} + \frac{d}{V_2}} = \frac{2}{\frac{1}{V_1} + \frac{1}{V_2}} \]