How do you find the kinetic coefficient of friction for this problem?

I'd use energy conservation, as I know the masses will cancel out. Friction = Fn * ?. Since no acceleration in the y direction, Fn = mg. So friction = mg?.

Initial energy (Kinetic energy) - Friction energy lost = 0.
At rest, the object will have no energy because it is not moving. All of the kinetic energy is lost from friction acting over the distance.

so..

1/2mv^2 = mg?X, Where X is the distance that friction acts... it's 1.4 m in this case.
masses cancel.
1/2v^2 = g?X.

? = (.5v^2) / (gX) = (.5*2^2)/(9.8*1.4) = (50/343) or approximately = .146 is your coefficient of friction.

The force due to friction is F = ?*m*g.
The amount of energy the book initially had is its kinetic energy = 1/2*m*v^2.
The amount of energy the book has at the end is zero. So we know the book lost 1/2*m*v^2 of energy.
Work done on an object is F*d (force*distance). The amount of work the friction did on the book (in the opposite direction of its sliding) is how the book lost its energy.

So,
?*m*g*d = 1/2*m*v^2. Divide both sides by m, then solve the equation for ?.

? = v^2/(2*g*d) = ((2 m/s)^2) / (2 * (9.8 m/s^2) * (1.4 m)) = .15 (no units).