Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag = kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity vo. Solution: a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as Σ = m ax Then: -m V = m since: a = dv/dt then -m V = m by integrating, we obtain the following expression: = voe Further, employing the rules of integration results to the following expression for position as a function of time x= (vo/ e as t+ 0, the position becomes x = vo/k b) To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows
Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag = kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity vo. Solution: a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as Σ = m ax Then: -m V = m since: a = dv/dt then -m V = m by integrating, we obtain the following expression: = voe Further, employing the rules of integration results to the following expression for position as a function of time x= (vo/ e as t+ 0, the position becomes x = vo/k b) To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
![Problem
Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as
Fdrag = kmv
where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling
with a velocity vo.
Solution:
a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as
F = -F
= m ax
Then:
-m
V = m
since:
a = dv/dt
then
-m
V = m
by integrating, we obtain the following expression:
= voe
Further, employing the rules of integration results to the following expression for position as a function of time
x= (vo/
- e
as t+ 0, the position becomes
x = vo/k
b) To solve for the velocity as a function of position v(X), we construct the net force in the x-axis as follows](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F141d3383-46e9-48f8-9833-dc5055d170cc%2Fa072632d-a198-4db7-be02-942d0bc01bae%2Fxyyw57_processed.png&w=3840&q=75)
Transcribed Image Text:Problem
Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as
Fdrag = kmv
where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling
with a velocity vo.
Solution:
a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as
F = -F
= m ax
Then:
-m
V = m
since:
a = dv/dt
then
-m
V = m
by integrating, we obtain the following expression:
= voe
Further, employing the rules of integration results to the following expression for position as a function of time
x= (vo/
- e
as t+ 0, the position becomes
x = vo/k
b) To solve for the velocity as a function of position v(X), we construct the net force in the x-axis as follows
![b) To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows
E F= -F
= m
Then:
-m
v = m
since:
a = dv/dt
then
-m
v = m
We can eliminate time by expressing, the velocity on the left side of the equation as
v = dx/dt
Then, we arrive at the following expression
= -k
By integrating and applying the limits, we arrive at the following
= Vo-
which, sows that velocity decreases in a linear maner.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F141d3383-46e9-48f8-9833-dc5055d170cc%2Fa072632d-a198-4db7-be02-942d0bc01bae%2Fhqyo1h_processed.png&w=3840&q=75)
Transcribed Image Text:b) To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows
E F= -F
= m
Then:
-m
v = m
since:
a = dv/dt
then
-m
v = m
We can eliminate time by expressing, the velocity on the left side of the equation as
v = dx/dt
Then, we arrive at the following expression
= -k
By integrating and applying the limits, we arrive at the following
= Vo-
which, sows that velocity decreases in a linear maner.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![Physics for Scientists and Engineers](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Lecture- Tutorials for Introductory Astronomy](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
![College Physics: A Strategic Approach (4th Editio…](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON