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Section 5.1 Distance and Accumulated Change Section 5.1: Distance and Accumulated Change Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Suppose a car is moving with increasing velocity and suppose we measure the car's velocity every two seconds, obtaining the data in Table 5.1: How far has the car traveled at most? How far has the car traveled at least? Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. (ft/sec) 60 76 40 60 88 76 96 100 420 ft 88 96 360 ft (sec) Can we improve our estimate? fig 5.2 page 238 Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Yes, if we know the velocity at more points in time. Figures 5.3 Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Figures 5.4 Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Figures 5.5 Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Figures 5.6 Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. A sports car accelerates from 0 ft/sec to 88 ft/sec in 5 sec. Find lower and upper bounds for the distance traveled in 5 seconds. 230 ft 318 ft In which time interval is the average acceleration greatest? Smallest? 0-1 sec has an average acceleration of 30 ft/sec2 4-5 sec has an average acceleration of 2 ft/sec2 Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. 70 m Velocity (m/sec) Find lower and upper bounds for the distance traveled in 5 seconds by an object whose velocity is given by the graph below. 130 m Time (sec) Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. 85 m Velocity (m/sec) Find lower and upper bounds for the distance traveled in 5 seconds by an object whose velocity is given by the graph below. 115 m Time (sec) AtFigures what time(s) is the acceleration zero? 5.6 2 and 4 sec Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Two cars start at the same time and travel in the same direction along a straight road. The figure below gives the velocity, v, of each car as a function of time, t. Which car reached the larger maximum velocity? A Which car traveled for the longer time? B Which car traveled the greater distance? A