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The velocity of an object was measured using a laser radar gun. The following data were collected. time (sec) 012345678 velocity (feet/sec)-1-10042341 You decide to plot these velocity data and connect successive data points with lines, as in the following graph. This graph determines a function vapproæ (t) that approximates the actual velocity function Vactual (t), which is unknown. By connecting data points with lines in the graph you are assuming that velocity is changing at a constant rate over one-second time intervals (or, equivalently, that acceleration is constant over one-second time intervals). This assumption may be incorrect because the actual rate of change of velocity may not be constant over one-second time intervals. However, you decide to use this graph anyway since it seems like a reasonable approximation to the actual velocity.

The velocity of an object was measured using a laser radar gun. The following data were collected. time (sec) 012345678 velocity (feet/sec)-1-10042341 You decide to plot these velocity data and connect successive data points with lines, as in the following graph. This graph determines a function vapproæ (t) that approximates the actual velocity function Vactual (t), which is unknown. By connecting data points with lines in the graph you are assuming that velocity is changing at a constant rate over one-second time intervals (or, equivalently, that acceleration is constant over one-second time intervals). This assumption may be incorrect because the actual rate of change of velocity may not be constant over one-second time intervals. However, you decide to use this graph anyway since it seems like a reasonable approximation to the actual velocity.

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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The velocity of an object was measured using a laser radar gun. The following data were collected. time (sec) 0 12345 678 velocity (feet/sec)-1-10042341 You decide to plot these velocity data and connect successive data points with lines, as in the following graph. This graph determines a function vappro (t) that approximates the actual velocity function vactual (t), which is unknown. By connecting data points with lines in the graph you are assuming that velocity is changing at a constant rate over one-second time intervals (or, equivalently, that acceleration is constant over one-second time intervals). This assumption may be incorrect because the actual rate of change of velocity may not be constant over one-second time intervals. However, you decide to use this graph anyway since it seems like a reasonable approximation to the actual velocity.
Transcribed Image Text:The velocity of an object was measured using a laser radar gun. The following data were collected. time (sec) 0 12345 678 velocity (feet/sec)-1-10042341 You decide to plot these velocity data and connect successive data points with lines, as in the following graph. This graph determines a function vappro (t) that approximates the actual velocity function vactual (t), which is unknown. By connecting data points with lines in the graph you are assuming that velocity is changing at a constant rate over one-second time intervals (or, equivalently, that acceleration is constant over one-second time intervals). This assumption may be incorrect because the actual rate of change of velocity may not be constant over one-second time intervals. However, you decide to use this graph anyway since it seems like a reasonable approximation to the actual velocity.
y 1.0 1,0 F1 Using this graph, you can estimate the displacement of the object after x seconds have elapsed by the value of the function s(x) Vapproa (t) dt. = Using the function s(x), answer the following questions about how far the object traveled. Your answers must include the correct units. Displacement after 2 seconds = Total displacement after 8 seconds = Total distance traveled over 8 seconds =
Transcribed Image Text:y 1.0 1,0 F1 Using this graph, you can estimate the displacement of the object after x seconds have elapsed by the value of the function s(x) Vapproa (t) dt. = Using the function s(x), answer the following questions about how far the object traveled. Your answers must include the correct units. Displacement after 2 seconds = Total displacement after 8 seconds = Total distance traveled over 8 seconds =
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