1. The problem statement, all variables and given/known data I'd like to understand Drag Force better; but school always ignores it. Thus, I'm asking this purely out of obssession. I'm picturing a scenario where a non-constant force is pushing an object horizontally, ignoring friction. But, I'd like to understand how Drag Force influences the object's velocity. My questions are: 1) Do the steps that I'm taking in my math make sense? 2) How do I interpret the math? 2. Relevant equations Let F(x) be a function of Force with respect to Displacement: F(x) = 200000 - 100x Force is decreasing linearly as displacement increases from 0 meters to 2000 meters. A quick google search led me to this formula: FD(x) = 0.5 * Drag Coefficient * Frontal Area of Object * Air Density * V2 Suppose I know the factors involved, and I get an overall constant of 0.18: FD(x) = 0.18v2 Let's assume the object has a mass of 70 kg. 3. The attempt at playing with math Finding Work: W(d) = ∫ from 0 to d of (200000-100x) dx = -50(d-4000)d Kinetic Energy: KE(d) = -50(d-4000)d = 0.5(70)v2 Solve for Velocity: v(d) = sqrt((2/70) * -50(d-4000)d) Plug velocity function into the Drag Force: FD(d) = 0.18(sqrt((2/70) * -50(d-4000)d))2 Net Force: F(d) - FD(x) = FNET(x) = [200000 - 100d] - [0.18(sqrt((2/70) * -50(d-4000)d))2] Here is where I feel like I did something wrong. When I integrate the Net Force to find Work and find the velocity function with respect to displacement all over again, the velocity decreases down to 0 at about 376 meters and continues to decrease into the negative numbers. However, originally the force acting on the object is a 2 kilometers influence. I don't think the object would suddenly go backwards at the 376 meter mark.