To find the final velocity of a car experiencing a decreasing drag force over a distance of 45 meters, the drag force equation, which is proportional to the square of the velocity, must be incorporated into Newton's second law. The discussion emphasizes the need to express the motion as a differential equation, transitioning from time to position as the independent variable for easier integration. Participants guide the original poster through the steps of setting up the equation, simplifying it, and preparing for integration. The process involves separating variables and applying the fundamental theorem of calculus, ultimately leading to the calculation of the final velocity. The conversation highlights the importance of careful algebraic manipulation and integration in solving the problem.
