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Math Help - What is the next step?

  1. #1
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    What is the next step?

    So the question is:

    Suppose an object moves along a horizontal path with the position function
    x(t) = 4t t^2 on the time interval 0 ≤ t 5, where x is measured in meters and t is measured in seconds. Find the instantaneous velocity of the object from t = 1. Use units to describe what this value means.

    I know that the first step is to find the derivative of the position function so:
    lim(delta x -> 0) [s(t + delta t) - s(t)] / [delta t]
    [((4t + delta t) - t^2) - (4t - t^2)] / [delta t]

    Now I don't understand how to simplify this so that I can plug in 1 for t?

    I'm sorry if this looks confusing.
    Any help is appreciated.
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  2. #2
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    Simply calculate the derivative? The velocity is indeed described by that, so:

    \frac{\partial (4t - t^2)}{\partial t} = 4 - 2t

    If you plug in t = 1 your derivative will be 4 - 2 = 2. The unit of this derivative is meters / second since you derived position (in meters) to time (in seconds).
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  3. #3
    MHF Contributor

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    Quote Originally Posted by iluvmathbutitshard View Post
    So the question is:

    Suppose an object moves along a horizontal path with the position function
    x(t) = 4t t^2 on the time interval 0 ≤ t 5, where x is measured in meters and t is measured in seconds. Find the instantaneous velocity of the object from t = 1. Use units to describe what this value means.

    I know that the first step is to find the derivative of the position function so:
    lim(delta x -> 0) [s(t + delta t) - s(t)] / [delta t]
    [((4t + delta t) - t^2) - (4t - t^2)] / [delta t]
    This is incorrect. What you want is \lim_{\Delta t\to 0}\frac{4(t+ \Delta t)- (t+ \Delta t)^2)- 4t+ t^2}{\Delta t}

    Multiply out 4(t+ \Delta t) and (t+ \Delta t)^2 and cancel what you can. You should be able to cancel everything in the numerator that does NOT have a " \Delta t" in it, factor \Delta t out of the numerator and cancel with the \Delta t.

    Now I don't understand how to simplify this so that I can plug in 1 for t?

    I'm sorry if this looks confusing.
    Any help is appreciated.
    Follow Math Help Forum on Facebook and Google+

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