Aerodynamic drag on vehicles: if A is the projected frontal area (m^2), V is vehicle speed (km/h), and C is a lumped constant, which proportionality correctly expresses wind resistance R for highway speeds?

Introduction / Context:
At typical highway speeds, aerodynamic drag is a major component of tractive resistance for road vehicles. Drag depends on fluid density, a shape-dependent drag coefficient, frontal area, and the square of speed. For practical calculations, these factors are often grouped into a single constant for given ambient conditions and vehicle type.

Given Data / Assumptions:

• R: wind (aerodynamic) resistance force.
• A: projected frontal area in m^2.
• V: speed in km/h (constant C absorbs unit conversions).
• C: lumped constant incorporating 0.5 * rho * C_d and unit factors.

Concept / Approach:
The fundamental relation is R = 0.5 * rho * C_d * A * v^2 (with v in m/s). When speed is expressed in km/h, a constant C converts units and embeds air density and C_d for the selected conditions, leading to R = C * A * V^2. The quadratic dependence on V explains why fuel economy deteriorates rapidly with speed.

Step-by-Step Solution:
Start with the standard drag equation in SI units. Convert the speed variable to km/h: absorb factors into a single constant C. Recognize the remaining functional dependence: proportional to A and V^2. Select R = C * A * V^2.

Verification / Alternative check:
Road-load coastdown tests fit tractive effort versus speed as F = a + bV + cV^2; the V^2 term corresponds to aerodynamic drag, reinforcing the quadratic relation across conventional speed ranges.

Why Other Options Are Wrong:

• Linear (C A V) understates drag growth; cubic (C A V^3) overstates force (power scales with V^3, not force).
• C^2 A V or (C V)/A: dimensionally inconsistent with force for fixed definitions.

Common Pitfalls:

• Confusing the cubic dependence of power (P = R * v ∝ V^3) with the quadratic dependence of drag force.

Final Answer:
R = C * A * V^2.