Solving Power Energy Problem: Inclined Plane 30 Degrees, 6.4m Long

[deviantdevil]

Q: An inclined plane at 30 degrees is 6.4m long. A book, which has a kinetic coefficient of friction with the incline of 0.2, is placed at the top and immediately begins to slide. Using energy considerations, how long will it take for the book to reach the bottom of the incline?

my solution is as follows:

6.4mg(sin(30))=0.5mv^2+0.2mg(cos(30))6.4
cancel out m and find v.
use vf^2=vi^2+2ad to find a
use d=vit+0.5at^2 to find t.

i think this solution works, but as you can see, it doesn't really "use energy considerations"...
any idea how i should go about solving this problem?

 

[JustinLevy]

i think this solution works, but as you can see, it doesn't really "use energy considerations"...

What did you use to get this line: "6.4mg(sin(30))=0.5mv^2+0.2mg(cos(30))6.4"

It looks to me like: initial potential energy = final kinetic energy + work done by friction
Why do you not consider that using energy arguments?

 

[deviantdevil]

i assumed the question to be asking for a solution that only requires energy arguments. as you can see, i go into Newtonian mechanics in the latter part of the solution. Is there a way to solve this question using energy/power alone?