Work, Energy and Power

A block of mass m = 1 kg,
moving on a horizontal surface with speed
vi
= 2 m s–1 enters a rough patch ranging
from x = 0.10 m to x = 2.01 m. The retarding
force Fr
on the block in this range is inversely
proportional to x over this range,
F
k
x
r =
−
for 0.1 < x < 2.01 m = 0 for x < 0.1m and x > 2.01 m
where k = 0.5 J. What is the final kinetic
energy and speed vf
of the block as it
crosses this patch ?