2. An experiment detects that a particle at $(1,0)$ (on the $xy$-plane) is moving towards the north at the speed $3$ meters per minute. At the same time another particle at $(-2,1)$ is moving towards the east at the speed $4$ meters per minute.

(a) $(5\%)$ Let $s(t)$ be the distance (in meters) between the two particles in $t$ minutes. $s(t)=\underline{\quad(3)\quad}$.

(b) $(10\%)$ Suppose at $t=t_0$ the two particles are closest to each other. Then $t_0=\underline{\quad(4)\quad}$.