average velocity

Question

A car covers first half of a distance at speed v1 and second half at speed v2. Average speed is:

RankGuru · Accepted Answer

Let the total distance be $2D$.
- Time taken for the first half: $t_1 = \frac{D}{v_1}$.
- Time taken for the second half: $t_2 = \frac{D}{v_2}$.
- Total time $T_{total} = t_1 + t_2 = \frac{D}{v_1} + \frac{D}{v_2} = D \left(\frac{v_1 + v_2}{v_1 v_2}ight)$.
- Average speed $v_{avg} = \frac{	ext{Total Distance}}{	ext{Total Time}} = \frac{2D}{D \left(\frac{v_1 + v_2}{v_1 v_2}ight)} = \frac{2 v_1 v_2}{v_1 + v_2}$.
This is the harmonic mean of the two speeds.

Rank Guru

average velocity

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