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

 

[tomcue]

Your approach is correct, however there may be some small errors in your calculations. It is always a good idea to double check your work and make sure all units are consistent throughout. Additionally, make sure you are using the correct values for mass and gravity in your calculation of the normal force (uk(mg)=max).

Another approach to solving this problem is to use the equation Ff = ukN to find the frictional force acting on the car. Since the car is skidding, the frictional force must be equal to the force of kinetic friction (Ff = Fk). From there, you can use the equation F=ma to find the acceleration of the car and then use the kinematic equation to solve for the initial velocity.

It is also important to note that the coefficient of kinetic friction (uk) may vary depending on the surfaces of the two cars involved in the collision. So, the answer you calculated may be slightly different from the actual initial velocity of the moving car.