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Math Help - help needed changing words to formula for integration

  1. #1
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    Post help needed changing words to formula for integration

    Hey guys,

    I know how to get the answer but I don't know what the formulas are

    The questions goes..

    You start at rest on a bike. You accelerate at 1 m/s^2 for 4 seconds and then travel at a constant velocity until you arrive at your destination which is 80 metres from the starting position. Calculate travelling time.

    I know I have to integrate twice to find the distance traveled during the acceleration period but I don't know what the formula for this question will be. I have a(t) = t ? But I don't get the correct answer when I integrate..

    I can do the question in my head easy but we have to use integration.

    Thanks
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  2. #2
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    Why can't you use the kinematic equations to solve this problem? Is there any instruction to solve this problem by integration?
    Last edited by sa-ri-ga-ma; September 12th 2010 at 05:41 AM.
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  3. #3
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    Just in case a picture helps, and if you do want or need to derive the formulae by integration from the definitions of velocity v and acceleration a in terms of displacement, s ...



    ... where straight lines are differentiating downwards with respect to t. Well, integrating a twice with respect to t ...



    Spoiler:


    Spoiler:


    So after 4 seconds the displacement is 8, and you've 72 metres to go, at 4 m/s.



    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; September 11th 2010 at 05:37 AM.
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  4. #4
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    Its for a calculus course I am doing so I just assumed they would want me to use calculus to find the answer.
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  5. #5
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    Quote Originally Posted by smplease View Post
    Hey guys,

    I know how to get the answer but I don't know what the formulas are

    The questions goes..

    You start at rest on a bike. You accelerate at 1 m/s^2 for 4 seconds and then travel at a constant velocity until you arrive at your destination which is 80 metres from the starting position. Calculate travelling time.

    I know I have to integrate twice to find the distance traveled during the acceleration period but I don't know what the formula for this question will be. I have a(t) = t ? But I don't get the correct answer when I integrate..

    I can do the question in my head easy but we have to use integration.

    Thanks
    I suggest that you start by drawing a velocity-time graph.
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  6. #6
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    No, a(t) is not t. You are told that the acceleration is 1 m/s^2 for 4 seconds- a(t)= 1. What is the velocity function at each time t for those 4 seconds? What will your velocity be at the end of the 4 seconds? What will your position be at the end of the 4 seconds? What distance do you still have to go to get to a total of 80 m? How long will that take at your new velocity?
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  7. #7
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    So during the period of acceleration.
    v = t and will be 4 m/s at the end of the period of acceleration.
    Displacement will be s = t^2/2. So displacement after 4 seconds will be 8 metres?
    Leaving 72 metres left to travel at constant velocity of 4 m/s, which would take 18 seconds and then add the time taken in the acceleration period of 4 seconds to get 22 seconds all up?
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  8. #8
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    Correct. Were you aware of the function of the 'spoiler' button, by the way?
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