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Direction of car's average acceleration vector as it turns

  1. Jan 13, 2014 #1
    1. The problem statement, all variables and given/known data

    A car, initially going east ward, rounds a 90 degree curve and ends up heading southward. If the speedometer reading remains constant, what's the direction of the car's average acceleration.



    3. The attempt at a solution

    a = Δv/Δt

    vi = (c,0)
    vf = (0,-c)

    (vf - vi )/Δt =(-c,-c)/Δt
     
  2. jcsd
  3. Jan 13, 2014 #2
    Is there a question here? This result looks correct. If they are asking for the direction, it's SW.
     
  4. Jan 13, 2014 #3

    Simon Bridge

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    Technically the answer should be given in terms of compass headings.
    I agree a question would be nice, then we don't have to guess the issue.

    Is it reasonable to guess that time into the corner is equal to time out of the corner?
     
  5. Jan 13, 2014 #4
    My answer tallies with the book except that instead of SW, I chose my answer in the form of Cartesian coordinate-much more empirical and non-arbitrary to me.

    So relative to the East and using the x-axis as East direction, the car is 225°
     

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  6. Jan 13, 2014 #5

    Simon Bridge

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    ... do you mean to ask if this is correct?

    Do you mean 225deg clockwise or anticlockwise from East?

    A compass bearing would be an angle measured clockwise from North, or it would be a name like "due N" or "NNE".

    225deg clockwise from due E would be NW - a bearing of -45deg.

    It is good practice to put the answer in the same terms that the question used ... so I'd pick "NW" rather than "-45deg" as the more appropriate of the two. It will make a difference to you marks in the coming years and to your employment prospects later.

    You seem to things it backwards:
    Cartesian coords are arbitrary and non-empirical - compass directions are the result of empirical physical phenomena. This is proved from the fact you can draw cartesian axis in any orientation without much in the way of physical constraints but you don't get to pick the direction the north-seeking pole of the compass needle points.

    Note: it helps us to help you if you ask questions: don't make us guess what you want.
     
    Last edited: Jan 13, 2014
  7. Jan 13, 2014 #6
    Sorry, I mis-typed it. It's 225° from the + x-axis.

    That made sense.
     
  8. Jan 13, 2014 #7

    Simon Bridge

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    Yes. Is this angle clockwise or anticlockwise? When you give this kind of answer in an exam, you have to say.

    If you gave the compass direction, instead, it would be clear.
    Was my compass direction "NW" correct for the direction of the average acceleration?
     
  9. Jan 13, 2014 #8
    SW.
    It's just strange that in Calculus class I didn't have to deal with the bearings. It would be implicitly assumed given that 225 is in the third quadrant and the convention was the +x-axis was the reference point.
     
  10. Jan 13, 2014 #9

    Simon Bridge

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    Actually it is an arbitrary convention common to many calculus classes, that the angle is taken anticlockwise from the +x axis ... just like you commonly use the right-handed Cartesian coordinate system. But that's only a convention and it will not be the same everywhere. Even in calc, different coordinate systems will have different definitions ... spherical polar has two angles for instance.

    Part of the question is testing to see if you can work with different conventions.
     
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