# 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,

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

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