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A particle moves on a horizontal line so that its position, in centimeters, at time t, in seconds, is given by s(t) = t³ 18t² + 96t+2, with t≥ 0. Assuming that the positive direction is to the right: A. Determine the velocity function, v(t). v(t) Evaluate v(7). v(7) = Interpret, with a complete sentence and appropriate units, the meaning of v(7) and its value.

A particle moves on a horizontal line so that its position, in centimeters, at time t, in seconds, is given by s(t) = t³ 18t² + 96t+2, with t≥ 0. Assuming that the positive direction is to the right: A. Determine the velocity function, v(t). v(t) Evaluate v(7). v(7) = Interpret, with a complete sentence and appropriate units, the meaning of v(7) and its value.

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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A particle moves on a horizontal line so that its position, in centimeters, at time \( t \), in seconds, is given by \[ s(t) = t^3 - 18t^2 + 96t + 2, \] with \( t \geq 0 \). Assuming that the positive direction is to the right: **A. Determine the velocity function, \( v(t) \).** \[ v(t) = \] *Evaluate \( v(7) \).* \[ v(7) = \] **Interpret, with a complete sentence and appropriate units, the meaning of \( v(7) \) and its value.** **B. Determine the \( t \)-interval(s) when the particle is moving to the right.** \[ \]
Transcribed Image Text:A particle moves on a horizontal line so that its position, in centimeters, at time \( t \), in seconds, is given by \[ s(t) = t^3 - 18t^2 + 96t + 2, \] with \( t \geq 0 \). Assuming that the positive direction is to the right: **A. Determine the velocity function, \( v(t) \).** \[ v(t) = \] *Evaluate \( v(7) \).* \[ v(7) = \] **Interpret, with a complete sentence and appropriate units, the meaning of \( v(7) \) and its value.** **B. Determine the \( t \)-interval(s) when the particle is moving to the right.** \[ \]
Expert Solution
Step 1: Given positio function of a particle

s left parenthesis t right parenthesis equals t cubed minus 18 t squared plus 96 t plus 2

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