Drag force proportional to speed squared

Steps:

• Recall the standard drag force formula: F = (1/2) C_d ρ A v^2.
• Rearrange to solve for C_d: C_d = 2F / (ρ A v^2), matching the given equation.
• Since C_d is unitless and constant for a shape, F must be proportional to v^2.
• Thus, the exponent n in F ∝ v^n is 2.

Why B is correct:

• The drag equation derives from fluid dynamics, where drag scales with v^2 for most vehicles.

Why the others are wrong:

• A: Linear dependence would imply F ∝ v, but equation shows v^2.
• C: Cubic scaling applies to rare high-speed cases, not standard cars.
• D: Quartic is unrelated to drag physics.

Final answer: B