# 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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