Problem 5 Suppose an object moves through a resisting medium with resistance proportional to its velocity v, so that d = -5v. dt 1. Find its velocity. Assume that it starts with zero initial velocity. 2. Find its position. Assume that it starts from zero initial displacement. 3. How far does it move before it almost stops. That is, find the limit of its position as t→∞0. Solution:

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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### Problem 5

Suppose an object moves through a resisting medium with resistance proportional to its velocity \( v \), so that \( \frac{dv}{dt} = -5v \).

1. **Find its velocity. Assume that it starts with zero initial velocity.**

2. **Find its position. Assume that it starts from zero initial displacement.**

3. **How far does it move before it almost stops. That is, find the limit of its position as \( t \to \infty \).**

**Solution:**
Transcribed Image Text:### Problem 5 Suppose an object moves through a resisting medium with resistance proportional to its velocity \( v \), so that \( \frac{dv}{dt} = -5v \). 1. **Find its velocity. Assume that it starts with zero initial velocity.** 2. **Find its position. Assume that it starts from zero initial displacement.** 3. **How far does it move before it almost stops. That is, find the limit of its position as \( t \to \infty \).** **Solution:**
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