Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity \(\mu\)) between two infinitely long horizontal plates separated by a distance \(2H\) as shown in the figure. The flow is driven by the combined action of a pressure gradient and the motion of the bottom plate at \( y = -H \) in the negative \( x \) direction. Given that \(\Delta P/L = (P_1 - P_2)/L > 0\), where \(P_1\) and \(P_2\) are the pressures at two \(x\) locations separated by a distance \(L\). The bottom plate has a velocity of magnitude \(V\) with respect to the stationary top plate at \(y = H\). Which one of the following represents the \(x\)-component of the fluid velocity vector?
