(Modeling) Braking Distance If aerodynamic resistance is ignored, the brak...

(Modeling) Braking Distance If aerodynamic resistance is ignored, the braking distance D (in feet) for an automobile to change its velocity from V₁ to V₂ (feet per second) can be modeled using the following equation.

K1 is a constant determined by the efficiency of the brakes and tires, K2 is a constant determined by the rolling resistance of the automobile, and u is the grade of the highway. (Source: Mannering, F. and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.)

(a) Compute the number of feet required to slow a car from 55 mph to 30 mph while traveling uphill with a grade of θ = 3.5°. Let K₁ = 0.4 and K₂ = 0.02. (Hint: Change miles per hour to feet per second.)

(b) Repeat part (a) withθ = -2°.

c) How is braking distance affected by grade θ? Does this agree with your driving experience?