B. Calculating instantaneous acceleration. 1. Using the data in Table II, calculate the instantaneous acceleration at the following intervals: i. t=5 ii. t = 15 iii. t = 25 iv. t=35 v. t=45 2. Explain how you used the limit definition of a derivative to calculate the instantaneous acceleration. Use your results to explain why the limit definition of a derivative is true. 3. At what point is the acceleration at a maximum? How is this relevant to the landing aircraft? For each of the questions above, provide supporting solutions and calculus terminology to explain how you arrived at your answers. Also, explain in detail what your answer represents in a real-world context and why this is useful. Part III: Analysis of Data - Applying Integrals A. Calculating total change (distance traveled) of the aircraft. B. 1. Using the data in Table I, use a right-endpoint estimate to calculate the distance traveled by the aircraft from t = 0 tot = 45 seconds. 2. Using the data in Table I, use a left-endpoint estimate to calculate the distance (total change) traveled by the aircraft from t = 0 to t = 45 seconds. 3. Find the best estimate for the distance traveled by the aircraft from t = 0 to t = 45 seconds. C. Graphing the model. Using the velocity data in Table I, generate a table of estimates that represents the total change of the moving object. Then, use this table of values to graph the model for the velocity function and the distance function. t in seconds 0 v(t) in feet per second 274.27 5 223.19 10 179.23 15 141.4 20 108.83 25 80.80 30 56.68 35 35.91 40 18.04 45 2.65 s(t) 0 Discuss the relevance of these graphs, and how the velocity graph is used to find the distance traveled by the aircraft. Discuss the relationship between the two graphs using calculus terminology. Prompt You have been hired by a firm that is designing a runway for an airport. Your job is to confirm that the runway is long enough for an airplane to land, but not unnecessarily long. You are given the velocity data for the largest aircraft that will land at the airport. The velocity data will be used to calculate the distance required for the aircraft to safely land and come to a stop. Below is a set of data that represents the velocity (in feet per second) of the final 45 seconds of the landing. At t = 0, the plane is on its final descent. X Table I t in seconds v(t) in feet per second 0 274.27 5 10 223.19 179.23 15 141.4 20 25 30 108.83 80.80 56.68 35 35.91 40 18.04 45 2.65 t in seconds v(t) in feet per second 4 5 232.8 223.19 14 148.52 Table II 15 24 141.4 86.08 25 80.80 34 35 44 45 39.82 35.91 5.55 2.65 Part I: Introduction Describe the purpose and problem statement of this report. How did you will use calculus to ensure that the runway is sufficient? How is the velocity data useful? Explain mathematically how the provided data was used to arrive at your final results. Part II: Analysis of Data - Applying Derivatives A. Calculating average acceleration Using the data in Table I, calculate the average acceleration for the following intervals: i. From t = 0 tot = 45 ii. From t = 25 tot = 45 iii. From t = 40 tot = 45