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CALCULATOR PERMITTED A test plane flies in a straight line with positive velocity v(t), in miles per minute at time t minutes, where v is a differentiable function oft. Selected values of v(t) for 0

CALCULATOR PERMITTED A test plane flies in a straight line with positive velocity v(t), in miles per minute at time t minutes, where v is a differentiable function oft. Selected values of v(t) for 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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CALCULATOR PERMITTED A test plane flies in a straight line with positive velocity v(t), in miles per minute at time t minutes, where v is a differentiable function oft. Selected values of v(t) for 0<t< 40 are shown in the table below 15 25 35 (min) 40 5. 20 (1)a (miles 9.5 7.0 4.5 2.4 2.4 4.3 7.3 7.0 9.2 per min) a. Find the average acceleration on the interval 5<t<20. Express your answer using correct units of measure. b. Based on the values in the table, on what interval(s) is the acceleration of the plane guaranteed to equal zero on the open interval 0<t<40? Justify your answer. c. Does the data represent velocity values of the plane moving away from its point of origin or returning to its point of origin? Give a reason for your answer. d. The function f, defined by f(t) = 6+cos(+3sin is used to model the velocity of the plane, in miles per minute, for 0 <t<40. According to this model, what is the acceleration of the plane at t%3D23? What does this value indicate about the velocity at t= 23? Justify your answer, indicating units of measure. 40
Transcribed Image Text:CALCULATOR PERMITTED A test plane flies in a straight line with positive velocity v(t), in miles per minute at time t minutes, where v is a differentiable function oft. Selected values of v(t) for 0<t< 40 are shown in the table below 15 25 35 (min) 40 5. 20 (1)a (miles 9.5 7.0 4.5 2.4 2.4 4.3 7.3 7.0 9.2 per min) a. Find the average acceleration on the interval 5<t<20. Express your answer using correct units of measure. b. Based on the values in the table, on what interval(s) is the acceleration of the plane guaranteed to equal zero on the open interval 0<t<40? Justify your answer. c. Does the data represent velocity values of the plane moving away from its point of origin or returning to its point of origin? Give a reason for your answer. d. The function f, defined by f(t) = 6+cos(+3sin is used to model the velocity of the plane, in miles per minute, for 0 <t<40. According to this model, what is the acceleration of the plane at t%3D23? What does this value indicate about the velocity at t= 23? Justify your answer, indicating units of measure. 40
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