Question

An auto travels for time 'T'. It travels with a uniform speed u in the first half and with a uniform speed of v in the second half of the given time interval. What will be the average speed of the train in the given time interval time 'T'?

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

Answer 1

The correct option is A $\frac{u+v}{2}$

The situation is shown in the diagram below:

For the first half time, distance travelled is:
$d_1=u\frac{T}{2}$

For the first half time, distance travelled is:
$d_2=v\times \frac{T}{2}$

Total distance:
$d=d_1+d_2$
$d=\frac{T}{2}(u+v)$

Average speed:
$v_{av}=\frac{d}{T}$
$v_{av}=\frac{\frac{T}{2}(u+v)}{T}$
$v_{av}=\frac{u+v}{2}$