$(10$ points$)$ A $30$ kg box initially at rest is pushed a distance of $3\mathrm{.}2$ m along a rough

horizontal floor with a constant force of $260$ N$.$ The coefficient of friction between the

box and the floor is $$k $=0\mathrm{.}41.$

a$)(2$ pts$)$ What is WP$,$ the work done by the applied force?

b$)(2$ pts$)$ What is Wf$,$ the work done by the frictional force?

c$)(2$ pts$)$ What is $$K$,$ the change in kinetic energy of the box?

d$)(4$ pts$)$ What is vf$,$ the final speed of the box?