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Suppose v(t) = 6t² - 3t on the interval [3, 5]. What is the displacement on [3, 5]? O 160 O 165 O 170 O 172 I

Suppose v(t) = 6t² - 3t on the interval [3, 5]. What is the displacement on [3, 5]? O 160 O 165 O 170 O 172 I

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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**Problem Statement:** Given the velocity function \( v(t) = 6t^2 - 3t \) on the interval \([3, 5]\), determine the displacement over this interval. **Question:** What is the displacement on \([3, 5]\)? 1. 160 2. 165 3. 170 4. 172 **Explanation:** To find the displacement, we need to integrate the velocity function \( v(t) \) over the interval \([3, 5]\). The displacement \( \Delta x \) over the interval \([a, b]\) is given by: \[ \Delta x = \int_{a}^{b} v(t) \, dt \] In this case, \( a = 3 \) and \( b = 5 \). Calculate the integral of \( v(t) = 6t^2 - 3t \) from 3 to 5 to find the displacement.
Transcribed Image Text:**Problem Statement:** Given the velocity function \( v(t) = 6t^2 - 3t \) on the interval \([3, 5]\), determine the displacement over this interval. **Question:** What is the displacement on \([3, 5]\)? 1. 160 2. 165 3. 170 4. 172 **Explanation:** To find the displacement, we need to integrate the velocity function \( v(t) \) over the interval \([3, 5]\). The displacement \( \Delta x \) over the interval \([a, b]\) is given by: \[ \Delta x = \int_{a}^{b} v(t) \, dt \] In this case, \( a = 3 \) and \( b = 5 \). Calculate the integral of \( v(t) = 6t^2 - 3t \) from 3 to 5 to find the displacement.
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