Foundations of Mathematical Reasoning, In-Class Activities, Lesson 13.B 93 Lesson 13, Part B, Breaking down a formula Theme: Civic Life In an earlier lesson, you determined that when you are driving 45 mph, you will travel 264 feet in 4 seconds, or 66 ft/sec. What if you apply the brakes? 1) Predict the braking distance, the distance the car will travel after the brakes have been applied. Credit: lon Chiosea/123RF Objectives for the lesson You will understand that: O A variable is a symbol that is used to represent a quantity that can change. O Some variables in a formula can be held fixed in order to analyze the effect that the change in one variable has on another. You will be able to: O Evaluate an expression. The formula for the braking distance of a car is d = 0. ,where %3D 2g(f +G) Vo = initial velocity of the car in feet per second (the velocity of the car when the brakes were applied) %3D d = braking distance (feet) G = roadway grade (percent written in decimal form) f = coefficient of friction between the tires and the roadway (0 < f < 1) (Note: Good tires on good pavement provide a coefficient of friction of about 0.8 to 0.85.) Constant: g = acceleration due to gravity (32.2ft / s or 9.8 m/s²) Since g is a constant, this formula has four variables. To understand the relationships between the variables. you will hold two of them fixed. That leaves you with two variables-one that will affect the other. Since you want to see how speed affects braking distance, you will hold the other two variables, f and G, fixed. Convright C 2016. The Charles A. Dana Center at the University of Texas at Austin Foundations of Mathematical Reasoning, In-Class Activities, Lesson 13.B 94 Consider a situation in which the coefficient of friction is 0.8 and the roadway grade is 2) 0.05. Write a simplified form of the formula using these values. 3) Calculate the braking distance when the speed is 45 mph (66 ft/sec). How does the distance compare to the prediction you made in question 1? 4) When the speed is 45 mph (66 ft/sec), calculate the braking distance when the roadway grade is 0.15 and 0.30. nsed efic leve beliogs 1ert (0+1ps onbieac er bnobeec leel dneo ert to yinolev heol) eon (mol lemi coo 100g0 (beiceU (280 of 8:0oda to noibh ed neewied noito to boog mee10 1AS SC-1vveng of eub e