The surface velocity of a river is measured at several locations \(x\) and can be reasonably represented by

\[ V=V_{0}+\Delta V\left(1-e^{-a x}\right) \]

where \(V_{0}, \Delta V\), and \(a\) are constants. Find the Lagrangian description of the velocity of a fluid particle flowing along the surface if \(x=\) 0 at time \(t=0\).