# Kinetic Friction to find velocity

1. Oct 20, 2008

### SuPaFly43218

1. The problem statement, all variables and given/known data

You have been called to testify as an expert witness in a trial involving an automobile accident. The speed limit on the highway where the accident occurred was 40 mph. The driver of the car slammed on his brakes, locking his wheels, and left skid marks as the car skidded to a halt. You measure the length of these skid marks to be 219 ft, 9 in., and determine that the coefficient of kinetic friction between the wheels and the pavement at the time of the accident was 0.400.

How fast was this car traveling (to the nearest number of mph) just before the driver hit his brakes?

2. Relevant equations

I would guess using the old formula of x1-x0 = (Vf^2-Vi^2)/2a would work. I am not sure how to find a though.

3. The attempt at a solution

0-66.9798 (that is the 219.75 ft converted to meters) = (0 - Vi^2)/2a

I am not sure where to go from here; please help! I know the answer is 51.2 mph, but I am lost on where to go.

Last edited: Oct 20, 2008
2. Oct 20, 2008

### SuPaFly43218

Bump! This is very important!

3. Oct 20, 2008

### LowlyPion

32.2 f/s2 is the acceleration from gravity. And they tell you the coefficient of friction is .4 of that.

So that yields your velocity in f/s from V2 = 2*a*x

Then to get mph divide by 1.46666.

Easy peasy. Nice and easy.

4. Oct 20, 2008

### SuPaFly43218

Right, i got the answer... but what is the formula a= (mu x g). I have never seen this formula before. Is this derived from something else??

5. Oct 20, 2008

### LowlyPion

F = u*m*g = m*a

a = u*g

6. Oct 20, 2008

### SuPaFly43218

Thank you, our physics book and teacher never explained that to us. Just to get this right, you said that (Force) F = mu x m (mass) x g (gravity)?

7. Oct 20, 2008

### SuPaFly43218

Nvm, i figured it out. Thank you for your help LowlyPion, your help is much appreciated.

8. Oct 20, 2008

### LowlyPion

The retarding force of friction divided by the normal force to the surface is the coefficient of friction.
That's what mu is.