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 `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 rangeis inversely proportional to x over this range ,
`F_(r) =(-k)/x "for " 0.1 lt x lt 2.01 m = 0 " for " x lt 0.1 m and x gt 2.01 ` where k 0.5 J .What is the final kinetic energy and speed `v_(f)` of the block as it crosses this patch ?

Explanation

`K_(f) = 2.8 J , v_(f) = 2.37 ms^(-1)`