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17-22. Position from velocity Consider an object moving along a line with the given velocity v and initial position. a. Determine the position function, for t≥ 0, using the antiderivative method b. Determine the position function, for t≥ 0, using the Fundamental Theorem of Calculus (Theorem 6.1 ). Check for agreement with the answer to part (a). 17. v(t) = sin t on [0, 2π]; s (0) = 1 18. v(t) = -t³ + 3t² - 2t on [0, 3]; s (0) = 4 19. v(t) = 6-2t on [0, 5]; s(0) = 0 - 20. v(t) = 3 sin πt on [0, 4]; s(0) = 1 21. v(t) = 9 — t² on [0, 4]; s(0) = -2 - 22. v(t): - - t + 1 on [0, 8]; s (0) = -4

17-22. Position from velocity Consider an object moving along a line with the given velocity v and initial position. a. Determine the position function, for t≥ 0, using the antiderivative method b. Determine the position function, for t≥ 0, using the Fundamental Theorem of Calculus (Theorem 6.1 ). Check for agreement with the answer to part (a). 17. v(t) = sin t on [0, 2π]; s (0) = 1 18. v(t) = -t³ + 3t² - 2t on [0, 3]; s (0) = 4 19. v(t) = 6-2t on [0, 5]; s(0) = 0 - 20. v(t) = 3 sin πt on [0, 4]; s(0) = 1 21. v(t) = 9 — t² on [0, 4]; s(0) = -2 - 22. v(t): - - t + 1 on [0, 8]; s (0) = -4

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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17-22. Position from velocity Consider an object moving along a line with the given velocity v and initial position. a. Determine the position function, for t≥ 0, using the antiderivative method b. Determine the position function, for t > 0, using the Fundamental Theorem of Calculus (Theorem 6.1 ). Check for agreement with the answer to part (a). 17. v(t) = sin ton [0, 2π]; s (0) = 1 18. v(t) = -t³ + 3t2 - 2t on [0, 3]; s(0) = 4 19. v(t) = 6 - 2t on [0, 5]; s(0) = 0 - 20. v(t) = 3 sin πt on [0, 4]; s(0) 21. v(t) = 9t² on [0, 4]; s(0) = -2 1 t +1 on [0, 8]; s(0) = -4 22. v(t) = = 1
Transcribed Image Text:17-22. Position from velocity Consider an object moving along a line with the given velocity v and initial position. a. Determine the position function, for t≥ 0, using the antiderivative method b. Determine the position function, for t > 0, using the Fundamental Theorem of Calculus (Theorem 6.1 ). Check for agreement with the answer to part (a). 17. v(t) = sin ton [0, 2π]; s (0) = 1 18. v(t) = -t³ + 3t2 - 2t on [0, 3]; s(0) = 4 19. v(t) = 6 - 2t on [0, 5]; s(0) = 0 - 20. v(t) = 3 sin πt on [0, 4]; s(0) 21. v(t) = 9t² on [0, 4]; s(0) = -2 1 t +1 on [0, 8]; s(0) = -4 22. v(t) = = 1
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