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Average speed question

  1. Jan 26, 2016 #1
    Hello,
    I was wondering if someone out there could help me. The question:

    The speed, v metres per second, of a particle is given as v=8sin2t+3cos2t
    where t is in seconds.
    i) Find the total distance travelled in the time interval 0≤t≤1
    ii) Find the average speed over this time interval.
     
  2. jcsd
  3. Jan 26, 2016 #2

    BvU

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    Hello Nicola, :welcome:

    This looks an awul lot like homework, and for that PF has a dedicated forum. With some rules: you need to show an attempt at solution and to use the template:

    1. The problem statement, all variables and given/known data
    The speed, v metres per second, of a particle is given as v=8sin2t+3cos2t
    where t is in seconds.
    i) Find the total distance travelled in the time interval 0≤t≤1
    ii) Find the average speed over this time interval.​

    2. Relevant equations
    ...
    3. The attempt at a solution
    ...
    Your turn! Help is on the way :smile:
     
  4. Jan 26, 2016 #3
    Here are the solutions:
     
  5. Jan 26, 2016 #4
    Hi,

    Believe it or not I am a teacher !! How embarrassing haha!
    We are having a debate about the solution to this question! IMG-20160124-WA0004.jpg IMG-20160124-WA0002.jpg

    I do not understand why the solution divides by 2 if you use the average value formula in integration to find average speed. If you substitute in values between 0 and 1 then the speed never goes above 3 point something so average speed can not be 7.03 but why divide by 2?
     
  6. Jan 26, 2016 #5

    BvU

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    Speed never goes below 3. Note that $$ 8\sin(2t)+3\cos(2t) = \sqrt{73} \; \sin (2t+\phi) \quad {\rm \ with \ \ } \cos\phi = {8\over \sqrt{73}} $$

    The division by 2 is a mistake by the author of the book.

    upload_2016-1-26_12-49-5.png
     
    Last edited: Jan 26, 2016
  7. Jan 26, 2016 #6
    Hi,

    Thank you. You may be able to help with one other question.

    Find the general solution solution of the equation sin2x=-√3/2 and use it to find all the solutions for 0°≤x≤360°.

    The solutions say that the answers are 120°,150°,300°,330°. I think that the solution set should be 0°≤2x≤360° for these to be the answers and that the answers should only be 120° and 150°.

    Thank you for your help.
    Nicola
     
  8. Jan 26, 2016 #7

    Samy_A

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    The solutions 120°,150°,300°,330° seem correct. These angles all lie between 0° and 360° and the sine of twice each of these angles is -√3/2.
     
  9. Jan 26, 2016 #8
    Sorry, I got confused with another question I was doing. The question was
    Find the general solution solution of the equation sin2x=-√3/2 and use it to find all the solutions for 0°≤x≤720°. ........NOT 360 as I had above.

    The solutions say that 120°,150°,300° and 330° but I think that the solutions should include 480°, 510°, 660° and 690° also unless the solution set is changed to 0°≤2x≤720° or 0°≤x≤360°
     
  10. Jan 26, 2016 #9

    Samy_A

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    I agree with you.
     
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