Question

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

• A. $\frac{u+v}{2}$
• B. $\frac{uv}{2}$
• C. $2uv$
• D. $uv$

Answer 1

The correct option is A

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

Step: Express total distance in terms of speed and time.
Total distance, $d=u\times$ $\frac{T}{2}+v\times \frac{T}{2}$
$d=\frac{T}{2}(u+v)$

Total time = T
Average speed $=V_{av}$ $=\frac{d}{T}$
$=\frac{\frac{T}{2}(u+v)}{T}$
$=\frac{u+v}{2}$