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Consider an object moving along a line with the following velocity and initial position. v(t) = - t³ + 6t? Determine the position function for t 0 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the methods. - 8t on [0,5]; s(0) = 5 To determine the position function for t20 using the antiderivative method, first determine how the velocity function and the position function are related. Chc the correct answer below. O A. The velocity function is the antiderivative of the absolute value of the position function. O B. The position function is the absolute value of the antiderivative of the velocity function. O C. The position function is the derivative of the velocity function. O D. The position function is the antiderivative of the velocity function. Which equation below will correctly give the position function according to the Fundamental Theorem of Calculus? O B. s(t) = s(0)+ J v(x)dx O A. s(t)= s(0)+ v(t)dt a O D. s(0) = s(t) + J v(x)dx O C. s(t) = J v(t)dt

Consider an object moving along a line with the following velocity and initial position. v(t) = - t³ + 6t? Determine the position function for t 0 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the methods. - 8t on [0,5]; s(0) = 5 To determine the position function for t20 using the antiderivative method, first determine how the velocity function and the position function are related. Chc the correct answer below. O A. The velocity function is the antiderivative of the absolute value of the position function. O B. The position function is the absolute value of the antiderivative of the velocity function. O C. The position function is the derivative of the velocity function. O D. The position function is the antiderivative of the velocity function. Which equation below will correctly give the position function according to the Fundamental Theorem of Calculus? O B. s(t) = s(0)+ J v(x)dx O A. s(t)= s(0)+ v(t)dt a O D. s(0) = s(t) + J v(x)dx O C. s(t) = J v(t)dt

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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Consider an object moving along a line with the following velocity and initial position. v(t) = -t +6t -8t on [0,5]; s(0) = 5 Determine the position function for t>0 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the methods. To determine the position function for t 0 using the antiderivative method, first determine how the velocity function and the position function are related. Chc the correct answer below. O A. The velocity function is the antiderivative of the absolute value of the position function. O B. The position function is the absolute value of the antiderivative of the velocity function. O C. The position function is the derivative of the velocity function. O D. The position function is the antiderivative of the velocity function. Which equation below will correctly give the position function according to the Fundamental Theorem of Calculus? O B. s(t) = s(0) + Į v(x)dx O A. s(t)=s(0)+ v(t)dt a O D. s(0) = s(t) + J v(x)dx O C. s(t) = J v(t)dt
Transcribed Image Text:Consider an object moving along a line with the following velocity and initial position. v(t) = -t +6t -8t on [0,5]; s(0) = 5 Determine the position function for t>0 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the methods. To determine the position function for t 0 using the antiderivative method, first determine how the velocity function and the position function are related. Chc the correct answer below. O A. The velocity function is the antiderivative of the absolute value of the position function. O B. The position function is the absolute value of the antiderivative of the velocity function. O C. The position function is the derivative of the velocity function. O D. The position function is the antiderivative of the velocity function. Which equation below will correctly give the position function according to the Fundamental Theorem of Calculus? O B. s(t) = s(0) + Į v(x)dx O A. s(t)=s(0)+ v(t)dt a O D. s(0) = s(t) + J v(x)dx O C. s(t) = J v(t)dt
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