A block of mass $m=1 \mathrm{kg}$ moving on a horizontal surface with speed $u=2 \mathrm{m} {\mathrm{s}}^{-1}$ enters a rough horizontal patch ranging from $x = 0.10 \mathrm{m}$ to $x = 2.00 \mathrm{m}$. If the retarding force $f_r$ on the block in this range is inversely proportional to $x$ over this range i.e.
$f_r=-\frac{k}{x}$ for $0.10<x<2.00$
$f_r=0$ for $x<0.10$ and $x>2.00$
If $k=0.5 \mathrm{J}$ then, the speed of this block ( in $\mathrm{m} {\mathrm{s}}^{-1}$ ) as it crosses the patch is ( use $\mathcal{l}n20=3$ )