Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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### Estimating Distance from Velocity Data When estimating distances from a table of velocity data, the time intervals don't need to be equally spaced. After a spaceship is launched, the following velocity data is recorded. Use this data to estimate the height above the Earth's surface at 123 seconds. #### Velocity Data Table | Time \(t\) (sec) | Velocity \(v\) (ft/s) | |------------------|-----------------------| | 0 | 0 | | 12 | 264 | | 17 | 374 | | 25 | 550 | | 41 | 902 | | 60 | 1320 | | 72 | 1884 | | 123 | 4281 | ### Instructions Calculate both a lower estimate and an upper estimate of the distance traveled using the given velocity data. - **Lower estimate of distance traveled**: Calculate using the minimum velocity over each interval - **Upper estimate of distance traveled**: Calculate using the maximum velocity over each interval **Formulas to Use**: Using the trapezoidal rule or considering endpoints of each interval helps in obtaining these estimates. #### Fill in your estimates below: - Lower estimate of distance traveled = [ ] miles - Upper estimate of distance traveled = [ ] miles
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Transcribed Image Text:### Estimating Distance from Velocity Data When estimating distances from a table of velocity data, the time intervals don't need to be equally spaced. After a spaceship is launched, the following velocity data is recorded. Use this data to estimate the height above the Earth's surface at 123 seconds. #### Velocity Data Table | Time \(t\) (sec) | Velocity \(v\) (ft/s) | |------------------|-----------------------| | 0 | 0 | | 12 | 264 | | 17 | 374 | | 25 | 550 | | 41 | 902 | | 60 | 1320 | | 72 | 1884 | | 123 | 4281 | ### Instructions Calculate both a lower estimate and an upper estimate of the distance traveled using the given velocity data. - **Lower estimate of distance traveled**: Calculate using the minimum velocity over each interval - **Upper estimate of distance traveled**: Calculate using the maximum velocity over each interval **Formulas to Use**: Using the trapezoidal rule or considering endpoints of each interval helps in obtaining these estimates. #### Fill in your estimates below: - Lower estimate of distance traveled = [ ] miles - Upper estimate of distance traveled = [ ] miles
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