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Suppose a(t) = (45/2)Vt + 2e -t, v(0) = -2, and s(0) = 7. Find s(t). s(t) =D %3D

Suppose a(t) = (45/2)Vt + 2e -t, v(0) = -2, and s(0) = 7. Find s(t). s(t) =D %3D

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** Suppose \( a(t) = \frac{45}{2} \sqrt{t} + 2e^{-t} \), \( v(0) = -2 \), and \( s(0) = 7 \). Find \( s(t) \). **Solution Requirements** To find \( s(t) \), integrate the acceleration function \( a(t) \) to determine the velocity \( v(t) \), and use the initial condition \( v(0) = -2 \). Integrate \( v(t) \) to find the position function \( s(t) \), using \( s(0) = 7 \) as an initial condition.
Transcribed Image Text:**Problem Statement** Suppose \( a(t) = \frac{45}{2} \sqrt{t} + 2e^{-t} \), \( v(0) = -2 \), and \( s(0) = 7 \). Find \( s(t) \). **Solution Requirements** To find \( s(t) \), integrate the acceleration function \( a(t) \) to determine the velocity \( v(t) \), and use the initial condition \( v(0) = -2 \). Integrate \( v(t) \) to find the position function \( s(t) \), using \( s(0) = 7 \) as an initial condition.
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