Can power (in the context of work and energy) ever be negative? Consider this question which HAS definitely been asked but i ask you now to question your first inclination to just 'do the question' and explain the thought process. Restrictions: assume you only know work energy theorem, and the definition of power (average power = force * average velocity OR DELTA work/ DELTA time, instantaneous work = force * instantaneous velocity or dW/dt) So no potential energy as it shouldn't require it. and of course you have your kinemtaic equations with newtons laws. 
"A 20.0-kg rock is sliding on a rough, horizontal surface at 8ms^-1
and eventually stops due to friction. The coefficient of
kinetic friction between the rock and the surface is 0.200. What
average power is produced by friction as the rock stops?" 
so, going the long route (instead of force * average velocity * cosTheta, where theta is angle between the two vectors)
work total = work done by friction
        = (1/2*m*v_2)^2 - (1/2*m*v_1)^2 (work-energy theorem)
        = -640J (Keep in mind that the work done by friction is negative as the the displacement and force are indeed in different directions)

time taken for work:
v = v_0 + at
t = (v - v_0)/a
= (0-8)/(-mu_k*g) (net acceleration worked out through newtons second law)
=4.08s
Therefore, average power should be
average power = DELTA work/ DELTA time
            = (-640J - 0J)/(4.08s - 0s)
            =-157watts

i double checked everything and looked at other websites and it gives no mention of negative power... so what do you guys think?
 A: Negative power in this context would mean the same thing as negative work: negative work means that the system - in this case, the block - is having mechanical energy stolen from it, just as positive work means it's acquiring energy. The negative power then just means the rate of losing energy, here to friction, just as positive power is the rate of accruing energy.
ADD: I looked again and note the wording of the question says "find the average power PRODUCED" by the sliding. So this will and should be positive, not negative, even though the power of the frictional force on the rock is negative. As we're now looking at it from the point of view of the external world, which sees the rock as producing energy (thus the world is accruing energy from the rock) in the form of heat and sound (and work, in destroying the surfaces that are rubbing together), not from the point of view of the rock, which is having energy stolen from it. If it had said "find the power of the frictional force on the rock", that power would be negative, but it says find the produced power, which is the power given to the outside world, and that is positive, and is the exact negative of the figure you calculated, so +157 W is the answer.
A: Assume that the system under consideration is the rock.  
So your statement 

Keep in mind that the work done by friction is negative

If perhaps better written as  

Keep in mind that the work done on the rock by the external force (friction) is negative

The work done on the rock is negative because the change in kinetic energy of the rock is negative.  
A negative amount of work done on the rock can be interpreted as a positive amount of work done by the rock.  
A: Yes, since power is rate at which work is done. So if work done is negative, time taken is positive, then power is negative. This would mean that the object is losing energy. On the other hand, positive power would mean that the object is gaining energy. Duality.
