Parametric, Polar and Vector-Valued Functions · Hard problem

A particle's position is $\mathbf{r}(t)=\langle t^2\sin(1/t)+2t,\;3t\rangle$ for $t\ne0$, and $\mathbf{r}(0)=\langle0,0\rangle$. The term $\sin(1/t)$ oscillates wildly near $t=0$. Does the particle still have a well-defined velocity vector at $t=0$, and if so, find its speed there.