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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Question #21 only, thank you!
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F627ffe10-a730-4e4c-b7e9-b306478e5985%2F3028b06f-c228-4dbe-95c3-58827ba6e31f%2F2ya9f4l_processed.jpeg&w=3840&q=75)
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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