Question

An auto travels the first half time with a uniform speed, $u$ and the next half time with a uniform speed, v Find its average speed for the complete journey.

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

Answer 1

The correct option is A

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

Express total distance in terms of speed and time:

Total distance, $d=u\times \frac{T}{2}+v\times \frac{T}{2}$

$\Rightarrow d=\frac{T}{2}(u+v)$ [$T$ is the total time]

Now, average velocity, $V_{av}=\frac{\text{Distance}}{\text{Time}}=\frac{d}{T}$

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

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