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Using your expression from the preceding problem. what is the terminal velocity? (Hint: Examine the limiting behavior: Does the velocity approach a value?)

$\mathbf{v}(t \rightarrow \infty) \rightarrow \sqrt{\frac{m g}{k}}$ to down

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:11

A body of mass $m$ is proj…

01:00

What is the acceleration o…

00:45

An object of mass m is rel…

02:20

Using your acceleration eq…

01:28

Calculate escape velocity,…

04:06

Resistance proportional to…

For the given velocity fun…

03:56

[T] Using your acceleratio…

01:05

01:58

Suppose the object in Prob…

English brother were asked to find a terminal velocity of a body on month on a new mission initial velocity V subzero with air resistance that is proportional to discover it of the velocity. Now, if you review page 16 dash to factor in the attack, we have this equation Ethical. That's a P minus f sub are We're This is our net Force s A p is the downward force and accept our is our resistance. This is a resistance came No, We know that the net force is the match times the derivative of velocity the Donald forces last times gravity And here we're told that resistance is proportional to the skirt of velocity. So what we have here is the constant key and discourage of ah, velocity be No, the DDT if we divined out my mouth would be equal to G minus Kate or over and times discourtesy How equal equilibrium point would be the terminal velocity. So if we set the sequel to zero so we get that B is equal to Ma times gravity over K square. This will be the terminals and its progress. So we have Let's call this miss a pickle Brown V sub Q Me somewhere here and we have will be subzero. Less than are really broom burn you. Then what we see happening is that the body's velocity will increase towards our it reappear button. If the subzero is above, they quickly bring point. Then we'll see that it drops down towards you being with us. What? It turned me out with us.

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