The U.S. Bureau of Public Roads determined the following characteristic total stopping distances D depending on the velocity of cars.
Speed M.P.H. (v) 20 30 40 50 60 70 80
Total Stop Distance D (ft) 42 73.5 116 173 248 343 464
a) Determine the best way to model the data. For example, by: a power function, an exponential function, or a polynomial. You may find it helpful to plot Ln(D) against both Ln(v) and v to see whether the data can be modeled by a power function or an exponential function.
b) Determine appropriate parameters for the model type chosen.
c) Calculate the relative error of your model.
d) Use the model to derive a simple formula for approximating the total stopping distance without a calculator. Illustrate the use of this formula by three examples.
The expert uses modelling and simulations to model data. A complete, neat and step-by-step solution is provided in the attached file.