Kinetic Friction to find velocity

[SuPaFly43218]

Homework Statement

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?

Homework 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.

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.

 

[SuPaFly43218]

Bump! This is very important!

 

[LowlyPion]

Homework Statement

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?

Homework 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.

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.

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.

 

[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??

 

[LowlyPion]

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??

F = u*m*g = m*a

a = u*g

 

[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)?

 

[SuPaFly43218]

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

 

[LowlyPion]

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)?

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