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05202012, 10:50 AM #1Medical Student
 Join Date
 May 2012
 Posts
 7
Stopping distance with only velocity and coefficient of friction
A car is traveling at 45.0 km/h on a flat highway. If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?
My question is what the free body diagram looks like. Is there a force in the direction in which the car is traveling, or just the opposing force of friction. ?

05292012, 01:14 PM #2
 Join Date
 Jun 2007
 Posts
 1,871
You need to make the assumption here that for the 'minimum distance' that the driver has hit the brakes and is no longer hitting the gas and so there is no force acting in the forward direction any longer, only the force of friction opposing the motion. From here you can see that the only horizontal force is friction and so it must equal ma. From here you can figure that a ~ 1m/s^{2}, or really 1m/s^{2} as it's opposite the velocity. In the attached image of the free body diagram you can see that the force of friction is to the left and this assumes that the initial velocity of 45km/hr is to the right. You'll need to convert 45km/hr to m/s which should give 12.5m/s and so since the car will slow down 1m/s every second (1m/s per second) then it will take 12.5 seconds to come to a complete stop.
Hope this helps!