A vehicle travels one-third of the total distance with speed $v$ and the remaining two-thirds of the

Question

A vehicle travels one-third of the total distance with speed $v$ and the remaining two-thirds of the distance with speed $2 v$. Its average speed is

Professor PC Thomas Classes · Answer

(a) : Let total distance be $s$. \ Time taken for the first one-third distance $= \frac{s/3}{v} = \frac{s}{3v}$. \ Time taken for the remaining two-thirds distance $= \frac{2s/3}{2v} = \frac{s}{3v}$. \ Total time taken $= \frac{s}{3v} + \frac{s}{3v} = \frac{2s}{3v}$. \ Average speed $=\frac{	ext{Total distance}}{	ext{Total time}} = \frac{s}{\frac{2s}{3v}} = \frac{3v}{2} = 1.5 v$