A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard's room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.
(1) $\frac { u + v } { 2 }$
(2) $\frac { 1 } { 2 } \sqrt { u ^ { 2 } + v ^ { 2 } }$
(3) $\sqrt { u v }$
(4) $\sqrt { \left( \frac { u ^ { 2 } + v ^ { 2 } } { 2 } \right) }$