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Math Help - Position Function Question

  1. #1
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    Position Function Question

    Here is the question:

    If the velocity function for a projectile is v(t) = 4 cos ( t), which of the following is a possible corresponding position function?

    Here is the answer:



    Could someone explain this to me? Thanks
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  2. #2
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    Hello vease1999
    Quote Originally Posted by vease1999 View Post
    Here is the question:

    If the velocity function for a projectile is v(t) = 4 cos ( t), which of the following is a possible corresponding position function?

    Here is the answer:



    Could someone explain this to me? Thanks
    v = \frac{ds}{dt}=4\cos(\pi t)

    \Rightarrow s = \int4\cos(\pi t)\,dt
    =\frac{4}{\pi}\sin(\pi t) + c
    So if the initial conditions are such that c = \frac{8}{\pi}, the solution would be:
    s = \frac{8+4\sin(\pi t)}{\pi}
    Grandad
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  3. #3
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    I was wondering if I could get a little more explanation on this. You'll have to bear with me. I'm pretty much at level 0. Thanks.
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  4. #4
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    Hello vease1999

    Velocity is the rate of change of position.
    v = \frac{ds}{dt}=4\cos(\pi t)
    So we integrate to find s.
    \Rightarrow s = \int4\cos(\pi t)\,dt
    Do you know how to integrate the cosine function?
    =\frac{4}{\pi}\sin(\pi t) + c
    c can have any constant value; for example \color{red}\frac{8}{\pi}.
    So if the initial conditions are such that c = \frac{8}{\pi}, the solution would be:
    s = \frac{8+4\sin(\pi t)}{\pi}
    Grandad
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