Solved

Physics: physical representation of the math

Posted on 2011-09-21
4
337 Views
Last Modified: 2012-05-12
r(t) is the position function of a particle moving in 2 or 3 space.

**I don't know how to do integral symbol, so I'll just denote that symbol as integ(f(x))**

integ( ||dr/dt|| ) from t0 to t1

I know dr/dt = v(t) which is the velocity function, and the norm of v(t) is the magnitude of the vector, aka, the numerical speed of the particle at time t, but when we integrate the speed, wouldn't we just end up with the position function again?

That is what my intuition is telling me, but my intuition has failed me before, so I would rather be shown why my thinking is wrong, if it even is. Thanks.
0
Comment
Question by:Zenoture
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 2
4 Comments
 

Author Comment

by:Zenoture
ID: 36578400
Wait, i think it just hit me as I posted the question.

If I were to assume some random value for || v(t) || to be 10 m/s, upon integration I would end up with 10t, where t is in seconds, and 10 is still in meters per second. So by simple plug and chug, where t = 1...

10 m/s * 1 s = 10m therefore proving that the above statement is the displacement of the particle after t seconds.


Right?
0
 
LVL 10

Accepted Solution

by:
abbright earned 167 total points
ID: 36578560
I believe this is true if the velocity is a straight one, that is only in one direction. If it isn't then the integral denotes the length of the way the particle has gone from t0 to t1, even if it was a circle and the particle ends up at the same point at t1 compared to when it started at t0.
0
 
LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 333 total points
ID: 36579798
It is important to note that in this entire discussion we are all integrating with respect to time.
The integral of dr/dt is of course (dr/dt)dt and so is just dr.
dr is the change in position so you are correct.

The indefinite integral of the velocity is the position function (of course were you to compute it, you would get that + C which would be the initial position).

The definite integral of the velocity is the displacement (distance from start to end).

0
 
LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 333 total points
ID: 36579808
Of course, if the velocity is not constant, then the integral would be the total distance traveled, not the final displacement (as abbright mentioned).
0

Featured Post

[Webinar] Code, Load, and Grow

Managing multiple websites, servers, applications, and security on a daily basis? Join us for a webinar on May 25th to learn how to simplify administration and management of virtual hosts for IT admins, create a secure environment, and deploy code more effectively and frequently.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
CAGR Calculation For SIP 13 105
Does a rhombus have 2 pairs of parallel sides 5 274
Smoothing a rectified sine wave DDS 32 155
Math equations 13 74
Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! https://www.google.com/about/careers/students/guide-to-technical-development.html How to Know You are Making a Difference at EE In August, 2013, one …
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

738 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question