A wind powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy, intercepted by its blade into electric energy. For wind speed v, the electrical power output will be proportional to
(Choose one among the four)
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In a unit of time, a unit of mass of wind will pass the blades. The wind has speed v, so the mass' kinetic energy is proportional to v^2. This energy is transfered in part to the blades, and it again proportional to v^2.
Since energy is conserved, and we're told the generator converts a fixed fraction, that fixed fraction of energy is still proportional to v^2.
The answer is v^2.
However, that is not exactly what I asked for. The question asked for the proportionality with the power, NOT Energy.
In my answer, I stated "In a unit of time"...this means an amount of energy proportional to v^2 has been transferred in this unit of time...that's power.