Consider the evolution of the radial position r(t) of a piece of plastic that, at some initial time t = 0, is dumped into the ocean along the coast (at r = R). By definition, the plastic's radial velocity is given by its change in radial position over time: ur dr/dt . (3)

Plug your expression for ur (r) = -1/6R*(r) into the differential equation (3) and solve for the general solution r(t). The solution r(t) is referred to as "general" because it will still depend on an arbitrary constant.