Atwood's machine acceleration Steps:

• Total mass on car side: passenger car + passenger = 520 kg + 80 kg = 600 kg.
• Counterbalance mass: 640 kg (heavier, so it falls and car rises).
• Net force: (640 kg - 600 kg) × g = 40g (downward on counterbalance side).
• Acceleration: a = net force / total mass = 40g / (600 kg + 640 kg) = 40 × 9.8 / 1240 ≈ 0.32 m/s².

Why A is correct:

• Follows Newton's second law for connected masses over a pulley: a = (m₂ - m₁)g / (m₁ + m₂), where m₂ = 640 kg > m₁ = 600 kg.

Why the others are wrong:

• B: Uses incorrect denominator m₂ only, giving a ≈ (40/640)g = 0.61 m/s² (approximation error for unequal masses).
• C: Might assume counterweight equals car (a ≈ 80g / 1040 ≈ 0.75 m/s², rounded wrongly).
• D: Far too small; perhaps divides by excessive total mass or neglects g.

Final answer: A