An auto travels the first halftime with a uniform speed $u$ and the next halftime with a uniform speed $v$ . Find its average speed.

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Solution

The correct option is A

Let $T$ be the total journey time.

Step: Express total distance in terms of speed and time.

Total distance $= d = d_{1} + d_{2} = (u \times$ $\frac{T}{2}) + (v \times \frac{T}{2})$

$d = \frac{T}{2} (u + v)$

Total time $= T$

$V_{a v} = \frac{d}{T}$

$= \frac{\frac{T}{2} (u + v)}{T}$

$= \frac{u + v}{2}$

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An auto travels the first halftime with a uniform speed u and the next halftime with a uniform speed v. Find its average speed.

The correct option is A Let T be the total journey time. Step: Express total distance in terms of speed and time. Total distance =d=d1+d2=(u× T2)+(v×T2) d=T2(u+v) Total time =T Vav=dT =T2(u+v)T =u+v2

An auto travels the first halftime with a uniform speed $u$ and the next halftime with a uniform speed $v$ . Find its average speed.