A vehicle travels half the distance with speed $v$ and the remaining distance with speed $2v$. Its average spe

Question

A vehicle travels half the distance with speed $v$ and the remaining distance with speed $2v$. Its average speed is

Accepted Answer

Average speed $v_{avg} = \frac{	ext{Total Distance}}{	ext{Total Time}}$. Let total distance be $2d$. Time $t_1 = d/v$, $t_2 = d/2v$. $v_{avg} = \frac{2d}{d/v + d/2v} = \frac{2d}{\frac{2d+d}{2v}} = \frac{2d}{\frac{3d}{2v}} = \frac{4v}{3}$.

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