Physics unit 5

A cart of mass m moves horizontally with a fan providing constant forward force F. Rolling resistance is negligible. Air drag has magnitude kv² and opposes motion, where v is speed and k is constant. The motion obeys m dv/dt = F−kv². In one run, F = 8 N and k = 0.5 N s²/m²; at v = 2 m/s the measured acceleration is 3 m/s². A speed-time graph rises smoothly from rest toward a limiting speed. A second fan setting doubles F while leaving the cart and k unchanged.