drive belt differentiation??

Question

a drive belt has a power P proportional to Tv - (w v^3)/g

v is speed of belt, T is tension and w is weight per unit length of the belt.

find the speed at which power is transmitted??

i am totally lost with this, the only thing i supposedly know is that differentiation is involved although i dont know what with respect to what.

Answer 1

I can't make much sense of the question, but I'll try anyway.
Speed at which power is transmitted (W/s) doesn't seem to be a physically meaningful quantity. Maybe what's wanted is the rate of change of power as v changes (dP/dv)?
If P = k (a constant) * (Tv - wv^3/g), then assuming T, w and g are also constants, dP/dv = k*(T - 3wv^2/g).
I hope this helps, but wouldn't be too surprised if it didn't.