A lecturer of mass 65.0 kg pushes a 12.0 kg cart carrying 7.0 kg of equipment. She pushes backward on the floor with 150 N and opposing forces total 24.0 N. Taking the whole group as the system, what is the acceleration?

1. Define the system as the lecturer, the cart and the equipment, since they accelerate as a unit. 2. By Newton's third law the floor pushes forward on the system with 150 N. 3. The opposing forces of 24.0 N act against that push, so the net external force is 150 N - 24.0 N = 126 N. 4. The mass of the system is 65.0 kg + 12.0 kg + 7.0 kg = 84 kg. 5. Newton's second law gives the acceleration as the net force divided by the mass. 6. Substitute the values: (126 N) / (84 kg) = 1.5 m/s^2. 7. Forgetting the opposing forces gives (150 N) / (84 kg) = 1.8 m/s^2, which is the trap. _Source: OpenStax College Physics (CC BY 4.0), Ch 4 "Dynamics: Force and Newton's Laws of Motion", section 4.4 Newton's Third Law of Motion: Symmetry in Forces_