Why it's hard to go fast

Bicyclists and other things that go fast must overcome air resistance, or drag, even to maintain a constant speed. A simple empirical model for the drag force on an object when the air flows smoothly around the object is \(\vec{F}_{Drag}=-c\vec{v}\), where \(\vec{v}\) is the velocity of the object and \(c\) is a constant that depends on the size and shape of the object. Consider a bicyclist putting out some power \(P_0\) (in watts) to overcome drag and maintain some constant speed \(v_0\). She then increases her speed to \(1.2 v_0\), which requires her to put out a power \(P_1\) to maintain. What is the ratio \(\frac{P_1}{P_0}\)?

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