A \(4 \mathrm{~m}\) diameter tank is filled with water and then rotated at a rate of \(\omega=2 \pi\left(1-\mathrm{e}^{-t}\right) \mathrm{rad} / \mathrm{s}\). At the tank walls, viscosity prevents relative motion between the fluid and the wall. Determine the speed and acceleration of the fluid particles next to the tank walls as a function of time.