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A particle travels along the horizontal axis such that its velocity, v(t), in meters per second, at time t is given by the function v(t) = 100 - for 0 sts 20. The position of the particle is given by x(t), and x(0) = 5. a) Find v '(12). Explain what this value indicates in terms of the context. b) Estimate the velocity of the particle at t = 12.1 seconds using a linear approximation at t = 12. c) Find the time k for which the average acceleration of the particle over the interval ksts 20 is-1 m/s. Justify your answer.

A particle travels along the horizontal axis such that its velocity, v(t), in meters per second, at time t is given by the function v(t) = 100 - for 0 sts 20. The position of the particle is given by x(t), and x(0) = 5. a) Find v '(12). Explain what this value indicates in terms of the context. b) Estimate the velocity of the particle at t = 12.1 seconds using a linear approximation at t = 12. c) Find the time k for which the average acceleration of the particle over the interval ksts 20 is-1 m/s. Justify your answer.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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A particle travels along the horizontal axis such that its velocity, v(t), in meters per second, at time t is given by the function v(t) = 100 - for 0 sts 20. The position of the particle is given by x(t), and x(0) = 5. a) Find v '(12). Explain what this value indicates in terms of the context. b) Estimate the velocity of the particle at t = 12.1 seconds using a linear approximation at t = 12. c) Find the time k for which the average acceleration of the particle over the interval k sts 20 is –1 m/s. Justify your answer. d) Write, but do not solve, an equation that gives the time n at which the particle will be at a position of 100 meters.
Transcribed Image Text:A particle travels along the horizontal axis such that its velocity, v(t), in meters per second, at time t is given by the function v(t) = 100 - for 0 sts 20. The position of the particle is given by x(t), and x(0) = 5. a) Find v '(12). Explain what this value indicates in terms of the context. b) Estimate the velocity of the particle at t = 12.1 seconds using a linear approximation at t = 12. c) Find the time k for which the average acceleration of the particle over the interval k sts 20 is –1 m/s. Justify your answer. d) Write, but do not solve, an equation that gives the time n at which the particle will be at a position of 100 meters.
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