The front point of a train moving with constant acceleration crosses a signal post with velocity u and the end point of the train crosses the signal post with velocity v. With what velocity the middle point of the train crosses the signal post ?

Question

$\begin{array}{1 1}(A)\;\large\frac{u+v}{2} \\(B)\;\sqrt {uv}\\(C)\;\sqrt{\frac{v^2-u^2}{2}}\\(D)\;\sqrt {\large\frac{v^2+u^2}{2}} \end{array} $