Find the position of the sprinter as a function of time, x(t), and show that the sprinter takes the time t = 6.3 s to reach the finish line at 100 m.

This time, 6.3 s, is much faster than Usain Bolt’s world record of 9.58 s (set in Berlin in 2009). In the real world, sprinters will be limited by air resistance. Let us now introduce a force model for air resistance, where we assume that the air resistance force D can be described as a quadratic polynomial:

Here ρ is the density of air, CD is the resistance coefficient, A0 is the cross-section ("surface") of the sprinter, v is the speed of the sprinter, and w is the speed of the air (wind). At sea level ρ = 1.293 kg/m3, for the sprinter's cross-section we assume A0 = 0.45 m2, CD = 1.2, and that there is no wind: w = 0 m/s. We now assume that the sprinter is only affected by the constant driving force F and the drag force D in the horizontal direction.