A thin $30cmx30cm$ flat plate is pulled at $3\frac{m}{s}$ horizontally through a $3\mathrm{.}6$ mm thick oil layer between two plates, one stationery and the other moving at a constant velocity of $0\mathrm{.}3\frac{m}{s}$ as shown in Figure $2\mathrm{.}1.$ The dynamic viscosity of the oil is $0\mathrm{.}27$ Pa$.$s$.$ Assuming the velocity in each oil layer to vary linearly,

a$)$ Plot the velocity profile and find the location where the oil velocity is zero.

b$)$ Determine the force that needs to be applied on the plate to maintain this motion.