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In physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters. The dark line is for a sphere with a smooth surface, while the lighter line is for the case of a rough surface. Drag depends on the properties of the fluid and on the size, shape, and speed of the object. Since the power needed to overcome the drag force is the product of the force times speed, the power needed to overcome drag will vary as the square of the speed at low Reynolds numbers and as the cube of the speed at high numbers.
Sometimes a body is a composite of different parts, each with a different reference areas, in which case a drag coefficient corresponding to each of those different areas must be determined. Note that the power needed to push an object through a fluid increases as the cube of the velocity. Since power is the rate of doing work, 4 times the work done in half the time requires 8 times the power. An object falling through viscous medium accelerates quickly towards its terminal speed, approaching gradually as the speed gets nearer to the terminal speed.