# Motion and friction

i've spent an hour reading this problem over and over again, trying to plug into the formulas but only came out with 2 or more unknown variables. I've not a clue to where to start, please help me.

Here goes..
during the investigation of a traffic accident, police find skid marks 90m long. They determine the coefficient of friction between the car's tires and the roadway to be .5 for the prevailing condition. Estimate the speed of the car when the brakes were applied.

choices are:
a. 9.49 m/s
b. 21
c. 29.7
d. 42

Here's how far i got .
givens:
d=90m
coeff=.5
vf=0
vi?

## Answers and Replies

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jamesrc
Gold Member
The only force on the car that you are supposed to consider after the brakes have been applied is kinetic friction between the tires and the road. Set ma = -&mu;N, where m is the mass of the car, a is the acceleration, &mu; is the coefficient of friction, and N is the normal reaction force of the ground to the car (equal in magnitude to the weight of the car). With a known constant acceleration and stopping distance, there is a kinematic formula you can use to find the initial velocity.

Here's a clue.

Are you stuck because they didn't give you the mass?

Look: the force exerted on the car by friction is &mu; times the normal force. In this case, on level ground the normal force is equal to mg. Now, you want to know the rate of deceleration (-acceleration), right? Well, assuming the only force affecting the car's speed was the braking force at the tires, F=ma so:
a = F/m
but here,
F = &mu;mg

OK?

Good timing, James.

jamesrc