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Math Help - Quadratic function to suit specifications?

  1. #1
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    Quadratic function to suit specifications?

    This is an assignment question I just cant seem to get. Its refering to the performance data of a car and you have to develop a function that incorporates a specified turning point and a speed that it must pass through at a certain time. Any help would be much appreciated
    So anyway, Im assuming that the function must pass through 0, 0 seeing as its a speed time graph. And it must travel through a speed of 27.7m/s at 7.7 seconds AND have a turning point at 78.3 seconds travelling at 63.05m/s..... I dont see how this is even possible in a quadratic funtion?
    The question doesnt specify a quadratic function but I figured it would have to be seeing its a speed time graph...
    Please help...
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  2. #2
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    Re: Quadratic function to suit specifications?

    Hey jbygo1.

    Can you explain in a little more detail what you are trying to do? Maybe a visual outlining what the car is doing?
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  3. #3
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    Re: Quadratic function to suit specifications?

    Hi,
    So the function is supposed to represent the performance of the car, so it shows its speed after t seconds. Its just a car accelerating as fast as possible in a straight line. So it says that it goes from 0 to 100km/h (27.77m/s) in 7.7 seconds and its max speed is 63.05m/s and it will take 78.3 seconds and were supposed to make a function that roughly represents the cars speed at any time while it is accelerating. Sorry if im not explaining it well..
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  4. #4
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    Re: Quadratic function to suit specifications?

    Is the acceleration constant over the whole period?
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  5. #5
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    Re: Quadratic function to suit specifications?

    No the acceleration changes at a constant rate
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  6. #6
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    Re: Quadratic function to suit specifications?

    The first thing you should do is integrate twice to get displacement and then solve for the co-efficients given your requirements.

    The displacement function as a function of time should be a quadratic in the typical form of f(t) = at^2 + bt + c
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  7. #7
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    Re: Quadratic function to suit specifications?

    I dont expect anyone to like write it out for me I just wanna know if its possible and how or if not then what other path could i go down? Periodic functions, a function with a higher power?
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  8. #8
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    Re: Quadratic function to suit specifications?

    Set c = 0 and then solve for your other variables given the velocity (27.7m/s at t = 7.7) by recalling that the velocity is the derivative of the distance function.
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  9. #9
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    Re: Quadratic function to suit specifications?

    What are you refering to as the coefficient sorry?
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  10. #10
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    Re: Quadratic function to suit specifications?

    The co-efficients are the a, b, and c variables in f(t).
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  11. #11
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    Re: Quadratic function to suit specifications?

    Ahh of course
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  12. #12
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    Re: Quadratic function to suit specifications?

    Hang on, That would make my speed time function a straight line but seeing as the acceleration is changing it simply cant be.
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  13. #13
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    Re: Quadratic function to suit specifications?

    It has 3 points it must run through, (0,0), (7.7, 27.7) and (78.3, 67.05) the last of which is the MAX speed.
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