What Was the Speed of the Car Based on Skid Marks and Kinetic Friction?

[jumptheair]

Homework Statement

You have been called to testify as an expert witness in a trial involving an automobile accident. The posted speed limit was 70 km/h . The driver of the car slammed on his brakes, locking the wheels, and left skid marks as the car skidded to a halt. You measure the length of these skid marks to be 61.9 m, and determine that the coefficient of kinetic friction between the wheels and the pavement at the time of the accident was 0.460. What was the speed of the car?

Homework Equations

fk = uk X n

The Attempt at a Solution

I have no clue on how to approach this problem. No velocity is given(speed limit is irrelavent i think) and only the displacement and the kinetic friction coefficient is given. And especially without the mass, i am clueless. Any help would be appreciated. Thanks.

 

[stewartcs]

Hint: The car's acceleration is assumed to be constant during the braking.

What equations does this fact allow you to use?

 

[stewartcs]

And especially without the mass, i am clueless.

The mass is irrelevant as you will see.


List what you know already:

Final velocity = 0 (the car has stopped)
Displacement = (x - x0) which is 61.9m

List what you don't know:
Car's acceleration, a

What you want to know:
Initial velocity, v

Now, assuming the acceleration is constant, what equation with the above variables can be used to find the initial velocity?

Once you have that equation all you will need is the unknown variable, a, in order to find v.

The other equation you have at your disposal is based on Newton's second law (Fnet,x = ma). Apply it your free body diagram (that hopefully you have already drawn...hint hint), and see what relationship do you come up with. I'll bet you'll see a way to find the acceleration that you are missing and also see why the mass of the car is irrelevant.

 

[jumptheair]

Got it. Thanks a lot!