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. \(\frac{2 v_{1} + v_{2}}{v_{1} + v_{2}}\)
3. \(\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}\)
4. \(\frac{L \left(\right. v_{1} + v_{2} \left.\right)}{v_{1} v_{2}}\)
Hint: The average speed is defined as the total distance divided by the total time.
Step 1: Find the time taken by the vehicle in two cases.
Time is taken to travel the first half distance \(t_1=\frac{1/2}{v_1}=\frac{1}{2v_1}\)
Time is taken to travel second half distance \(t_2=\frac{1}{2v_2}\)
Total time \(t_1+t_2\) = \(\frac{1}{2v_1}+\frac{1}{2v_2}\) = \(\frac{1}{2}[\frac{1}{v_1}+\frac{1}{v_2}]\)
Step 2: Find the average speed.
\(V_{avg}\)
= \(\frac{2v_1v_2}{v_1+v_2}\)
Hence, option (3) is the correct answer.
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