Physics

Work done by a variable force is the integral of force over distance—you can't just multiply $F \times d$ when the force changes. The key insight is that $W = \int F \, dx$ captures how the force's magnitude and direction change along the path. Since this force is negative (resistive), you expect negative work, meaning the force opposes motion and removes energy from the system.

Work done by a variable force is the integral of force over distance—you can't just multiply $F \times d$ when the force changes. The key insight is that $W = \int F \, dx$ captures how the force's magnitude and direction change along the path. Since this force is negative (resistive), you expect negative work, meaning the force opposes motion and removes energy from the system.