# In the case of uniformly accelerated motion along a straight line , why do we write average velocity = (u+v)/2 , where u =initial velocity and v = final velocity .

Dear Student,

Please find below the solution to the asked query:

Average velocity is written as the ratio of the total displacement and time interval.

$S=Ut+\frac{1}{2}a{t}^{2}\phantom{\rule{0ex}{0ex}}So,\phantom{\rule{0ex}{0ex}}\Rightarrow {V}_{avg}=\frac{S}{t}=\frac{Ut+{\displaystyle \frac{1}{2}}a{t}^{2}}{t}=U+\frac{1}{2}\left(\frac{V-U}{t}\right)t\phantom{\rule{0ex}{0ex}}\Rightarrow {V}_{avg}=U+\frac{V}{2}-\frac{U}{2}=\frac{V}{2}-\frac{U}{2}\phantom{\rule{0ex}{0ex}}\Rightarrow {V}_{avg}=\frac{V-U}{2}$

Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards

**
**