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Spokesperson Strategy Analyst: Critical Thinking Question: to be agreed upon by the group, and written below by the recorder. For the bicycle in Model 1, write down an integral that gives the change of position fromt 6 tot 10. Give an estimate of the value of this integral based on work done in the activity and explain how you got your estimate. Be sure to write complete sentences, and include your printed first and last names, and UIDs. 10 For instructors use only 216 Integration 4: The Fundamental Theorem of Calculus 14: Fundamental Theorem of Calculus (FTC) Model 1: A High-Wire Act e v(n) negative The graph at right plots the velocity v() of a circus performer during a high-wire bicycle act. At 1=0 she is 2 feet from the starting platform. Construct Your Understanding Questions3 1. Based on the picture and the graph, over4 what time interval is the bicycle moving forward? ..moving backward? At 1 = 0 s, the bicycle's position-distancefrontestartingplatform-a-ft. At i-1O s the bicycle is farthest from the starting platform and its velocity-O.fi's 2. 3. (Check your work) Are your answers above consistent with the fact that at 6 s the bicycle is ues momentarily stationary? If'not, check your understanding of Model . 4. Recall that when v) is positive, the area between the graph of y ) and the f-axis from a to b is equal to distance traveled between-aand t =b. a. On the graph in Model 1 (above), shade the area equal to the distance traveled between -oand-2s. Use the grid to estimate this value =-4 feet b. On the axes below-right, plot the bicycle's position at 2 s. Note that position is defined as the distance from the starting platform. (The point at Now add shading to the graph in Model 1 so the total shaded area 18 equals the distance traveled between 16 0 is given.) c. 0 and 1-4s. This value-2f On the axes at right, plot the bicycle's position at 14s 14t 12 10 d. e. Add shading to Model 1 so the total shaded area equals the distance traveled between 1-0 andに6 s. Estimate this value On the axes at right, plot the bicycle's position at -6s -2 f. 10 11 The definite integrals v) dt-4 and) dt 12 are associated with parts a. and c. of the previous question. Give the definite in 5. tegral (and estimated value) that is associated with part e POGIL

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