A block of mass 1 kg, moving along x with speed v_i=10 m / s enters a rough region ranging from x=0.1 m to x=1.9 m. The retarding force acting on the…

A block of mass $\displaystyle 1$ kg , moving along $\displaystyle x$ with speed $\displaystyle v_i=10 \mathrm{~m} / \mathrm{s}$ enters a rough region ranging from $\displaystyle x=0.1 \mathrm{~m}$ to $\displaystyle x=1.9 \mathrm{~m}$. The retarding force acting on the block in this range is $\displaystyle \mathrm{F}_{\mathrm{r}}=-\mathrm{k} x \mathrm{~N}$, with k $\displaystyle =10 \mathrm{~N} / \mathrm{m}$. Then the final speed of the block as it crosses rough region is.