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Homework Help: Drawing direction fields

  1. Aug 5, 2008 #1

    XSK

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    1. The problem statement, all variables and given/known data

    (i'm not sure if this is the correct forum please move it if incorrect)
    my problem is with generally drawing direction fields - i dont really know what to do. i have notes but i can't make head nor tail of them. this is an example of a question concerning them:

    veloc.png

    2. Relevant equations

    i know that if you stick the requirments into newton's 2nd law adding constant k you get that equation, and i know to find the terminal velocity you integrate and find v, but i dont know how to sketch the direction field.

    3. The attempt at a solution

    i see that

    dv/dt = -g + k/m

    but this seems to be independant of both v and t so how do i plot it as a graph?

    even if there were a v or t in that equation i still wouldn't be comfortable to draw the direction field because i don't know what to do >_>;

    thanks
     
    Last edited: Aug 5, 2008
  2. jcsd
  3. Aug 5, 2008 #2
    Think of direction fields as a [tex]{dy \over dx} = f(x,y)[/tex]. At each point [tex](x,y)[/tex] on the graph, you draw a tic-mark with slope equal to f(x,y). So here, instead of x and y, we have v and t, and f(v,t)=-g+k/m. What's the slope of each tick mark going to be?
     
  4. Aug 8, 2008 #3

    XSK

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    uhh
    i'm not sure....some kind of straight line?
     
  5. Aug 8, 2008 #4

    HallsofIvy

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    Science Advisor

    Check the meaning of the word "slope". It is a number not "some kind of line". What does the slope of a line mean?
     
  6. Aug 12, 2008 #5

    XSK

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    ok i looked up slope and now know it is a number but the answer to this question still eludes me!

    i dont know how you'd put the equation on a graph

    the notes i have for this involve looking at the independence of say, x of the equation so im rather stumped. also i just suck at graphs...
     
    Last edited: Aug 12, 2008
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