Hat is the coefficient of kinetic friction between the floor and the box

[Nayeli MTZ]

I have no idea of how to start solving this problem.
A 5kg box slides 3m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3m/s?
Can somebody please help me solve the problem?

 

[Astronuc]

We respectfully request students to show their work.

Now since the box has an initial velocity, it has kinetic energy. It has mass, and therefore a weight, and therefore a frictional force (in a gravitational field).

Use conservation of energy and the fact that force applied over distance is equivalent to energy. When the box stops, it has not kinetic energy. What happened to the initial kinetic energy?

 

[Nayeli MTZ]

I have no idea, it is one of my HMK problems from Physics. It is a multiple choice question, the choices are 1.05,0.587,0.153,0.306, and 0.2

 

[Nayeli MTZ]

I think this is how it is solved.
F_k=mv²/d
F_k=15
\mu=F_k/mg
\mu=0.306

 

[Astronuc]

Please show how one derived those relations, particularly F_k=mv²/d. And please show the values one assumes.

There appears to be a factor of 2 missing.