Kinetic Friction of moving car hitting a stationary car

[orange03]

Homework Statement

A police officer investigating an accident estimates from the damage done that a moving car hit a stationary car at 24 km/h. If the moving car left skid marks 47 m long, and if the coefficient of kinetic friction is 0.68, what was the initial speed of the moving car? (The answer is in km/h.)

Homework Equations

F=ma
Vx^2=Vox^2+2ax(deltax)

The Attempt at a Solution

I found acceleration by putting uk(mg)=max. I got 6.66 m/s^2 for acceleration. I plugged it into the kinematic equation Vx^2=Vox^2+2ax(deltax) and got 24.11 m/s for initial velocity. Then, I converted it into km/h and got 86.81 km/h. But, the answer is wrong and I don't know how to do it the correct way.

 

[rock.freak667]

I'd use conservation of energy.

Work done by friction = change in kinetic energy of the car

W_f=u_kN