Problem 7-62 Energy cons. with friction

A pen of mass \(0.057\; kg\) is sliding across a horizontal desk. In sliding \(25\; cm\), its speed decreases to \(5.7 \;cm/s\). What was its initial speed if the force of kinetic friction exerted on the pen by the desk is \(0.15\; N\) in magnitude? Use conservation of energy.

FBD with all forces and directions indicated.

In the motion of the pen:

(A)   Momentum is conserved.

(B)   Mechanical energy is conserved.

(C)   Total energy (including thermal) is conserved.