Energy proportional to speed squared due to resistive force

Steps:

• Resistive force F ∝ v², so total energy E = F × distance = k v² d, where d is fixed at 80 km.
• For 70 km/h, E = k (70)² × 80.
• For 60 km/h, E' = k (60)² × 80.
• Ratio E'/E = (60/70)² = (6/7)² = 36/49 ≈ 0.73.

Why A is correct:

• Work-energy principle: energy equals resistive force times distance, and F ∝ v² implies E ∝ v² for constant d.

Why the others are wrong:

• B: Underestimates ratio; (60/70) ≈ 0.857, but squared gives 0.73, not linear.
• C: Inverse of ratio; would apply if E ∝ 1/v², but resistance increases with v².
• D: Overestimates; (70/60)² ≈ 1.36, but that's for higher speed, not lower.

Final answer: A