Vehicle Aerodynamics — Predicting Drag with Speed Changes A passenger car experiences an aerodynamic (air) resistance of R at a speed of 20 km/h. Assuming all other conditions remain the same and the flow is in the usual road-vehicle regime where aerodynamic drag varies with the square of speed, what will the air resistance be at 40 km/h?

Introduction / Context:
Aerodynamic drag is a major road load on vehicles at moderate to high speeds. Understanding how drag scales with speed helps in estimating power demand, fuel economy, and acceleration performance. This question tests the classic proportionality of drag with the square of velocity.

Given Data / Assumptions:

• Baseline speed v1 = 20 km/h produces drag R.
• New speed v2 = 40 km/h.
• Same frontal area, drag coefficient, and air density (no wind, same altitude).
• Rolling resistance and drivetrain losses are not part of the asked change; only aerodynamic force is considered.

Concept / Approach:
The aerodynamic drag force on a vehicle is modeled as Fd = 0.5 * rho * Cd * A * v^2. Holding rho, Cd, and A constant, Fd is directly proportional to v^2. Therefore, when speed doubles, the drag force becomes four times the original value.

Step-by-Step Solution:
Let Fd1 = k * v1^2 = R, where k = 0.5 * rho * Cd * A.At v2 = 2 * v1, Fd2 = k * (2 * v1)^2.Compute: Fd2 = k * 4 * v1^2 = 4 * (k * v1^2) = 4R.Hence, the new aerodynamic resistance is four times the original.

Verification / Alternative check:
Power required to overcome drag is P = Fd * v, which scales as v^3. Doubling speed would require about eight times the power, consistent with drag quadrupling and speed doubling.

Why Other Options Are Wrong:
R: Implies drag independent of speed, incorrect.2R: Would be true if drag were proportional to v (linear), not v^2.4 R^2: Dimensional nonsense; squaring force is meaningless here.R/2: Opposite of the actual trend.

Common Pitfalls:
Confusing drag force (proportional to v^2) with required power (proportional to v^3).Ignoring the assumption that coefficients and air density remain constant.

Final Answer:
4R