Can force or displacement be negative in the work equation?

[SkyrimKhajiit]

I know that work is the "dot product" of force and displacement, but I got a little stuck with this problem:

"Vera is driving her 1000-kg car at a speed of 8m/s. When Vera slams on the brakes, the ground exerts an 8000-N frictional force to bring the car to a stop. Determine the initial kinetic energy of the car, the work done by friction on the car, and the stopping distance of the car."

So of course by simple computation, you'd get:

W_ext=KE_f-KE_i
W_ext=-32,000J

But then I plug it into the equation W=F*d*cos(theta):

(-32,000J)=(-8000N)(d)(-1)

Which would mean that d=-4m...but it isn't, since the car is moving in a straight line, then slowing to a stop, correct? This is where I got confused--the dot product means you ignore the directions of force and displacement, but does it also mean you ignore whether it's positive or negative? Or does that in itself denote direction?

 

[CWatters]

I think the problem is that you have double counted the direction of the force F as negative. eg You have it negative because it's pointing backwards AND you have the angle as Cos(180) which is -1.

 

[Orodruin]

You are taking the force to be both negative and with an angle that is 180 degrees, which is another negation, and you end up with a positive force. You have to decide whether you consider the force negative or the angle to be 180 degrees.