A block of mass m = 1 kg moving on a horizontal surface with speed v _i = 2 ms^–1 enters a rough patch ranging from x = 0.10 m to x = 2.01 m. The retarding force F_r on the block in this range is inversely proportional to x over this range
$F_r=\frac{k}{x}$ for 0.1 < x < 2.01 m
     = 0 for x < 0.1 m and x > 2.01 m
where k = 0.5 J. What is the final K.E. and speed v_f   of the block as it crosses the patch?
$\nu$