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:
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:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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