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Math Help - Speeding up/Slowing down from graph

  1. #1
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    Speeding up/Slowing down from graph

    Hi, I forget how to tell when a velocity graph is speeding up or slowing down.
    Below is the image, where I have to put where it is speeding up/slowing down in interval notation.

    I thought it was speeding up between (0,1) because it has positive slope there and slowing down from (1,3). Can someone correct my logic? Any help would be great, I've literally googled/looked at my textbook and both didnt help me.
    Attached Thumbnails Attached Thumbnails Speeding up/Slowing down from graph-3-7-005a.gif  
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Speeding up/Slowing down from graph

    Well, it depends what "speeding up" means. Usually in problems like this they ask you to show where the veliocity is increasing and where it is decreasing. If that's what they want, then you have it correct - velocity increases if the slope of the velocity graph is positive. However, if they really use the terms "speeding up" and "slowing down" in the question then we have a problem, as in general usage "speed" is a scalar, not a vector. Consequently "speeding up" means that the absolute value of velocity is increasing, and "slowing down" means the absolute value of the velocity is decreasing. Here from t = 2 to t = 3 as the velocity becomes more negative that would be thought of as speeeding up in the negative direction. So - please confirm the wording of the question, and tell us whether that changes your answer or not.
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  3. #3
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    Re: Speeding up/Slowing down from graph

    It says "When is the particle in figure (a) speeding up? (Enter your answer using interval notation.)"
    However, my above answer was wrong. So, according to your wording it would be slowing down at (3,4)?
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    Re: Speeding up/Slowing down from graph

    speeding up when velocity and acceleration have the same sign ... 0 to 1 and 2 to 3

    slowing down when velocity and acceleration have opposite signs ... 1 to 2
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    Re: Speeding up/Slowing down from graph

    velocity is positive above the x axis and acceleration is negative when v(t) has a negative slope, so that makes sense now for (1,2)
    I think I'm sort of getting it now...but heres another graph

    In this case I thought it would speed up (1,2) and (3,4)
    but slow down (0,1) & (2,3). Is this correct? I drew a chart and put + or - for acceleration & velocity.
    Attached Thumbnails Attached Thumbnails Speeding up/Slowing down from graph-3-7-005b.gif  
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  6. #6
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    Re: Speeding up/Slowing down from graph

    Quote Originally Posted by katiebear128 View Post
    velocity is positive above the x axis and acceleration is negative when v(t) has a negative slope, so that makes sense now for (1,2)
    I think I'm sort of getting it now...but heres another graph

    In this case I thought it would speed up (1,2) and (3,4)
    but slow down (0,1) & (2,3). Is this correct? I drew a chart and put + or - for acceleration & velocity.
    you broke the code ...
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  7. #7
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    Re: Speeding up/Slowing down from graph

    ahhh sorry whats the code? Im new to this site...am I supposed to start a new thread?
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  8. #8
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    Re: Speeding up/Slowing down from graph

    Quote Originally Posted by katiebear128 View Post
    ahhh sorry whats the code? Im new to this site...
    "broke the code" = "get the idea"
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  9. #9
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    Re: Speeding up/Slowing down from graph

    oh, haha great! yay! Sorry that was slow of me, i cant do math & write at the same time apparently But thanks for your help, I appreciate it
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