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Math Help - Find the Average Velocity

  1. #1
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    Find the Average Velocity

    The position function s of a point P moving on a coordinate line l is given, with t in seconds and s(t) in centimeters.

    (a) Find the average velocity of P in the following interval [1, 1.2].

    (b) Find the velocity of P at t = 1.

    s(t) = 4t^2 + 3t
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Find the Average Velocity

    a) Average velocity is  v_{avg} = \frac {\Delta s}{\Delta t}. So determine s(1.2)-s(1.0) and divide by  \Delta t = 0.2 seconds.

    b) Given the position function s(t), the velocity equations is  v(t) = \frac {ds(t)}{dt} . Evaluate for t=1.0.
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  3. #3
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    Re: Find the Average Velocity

    a) I got average velocity = 11.8

    b) I am confused to do it.
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    MHF Contributor ebaines's Avatar
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    Re: Find the Average Velocity

    Quote Originally Posted by joshuaa View Post
    a) I got average velocity = 11.8
    Good!

    Quote Originally Posted by joshuaa View Post
    b) I am confused to do it.
    The velocity of the particle at t=1 is equal to the slope of the s(t) curve at t=1. I suggested calculating the derivative to find that slope - have you taken any calculus classes where you have learned about derivatives? If not, then you could plot the graph of s=4^2+3t and use a straight edge to estimate its slope at t=1. Alternatively, you could use the same approach as in part (a) to find the average velocity between two points that are very close to t=1; for example if you calculate the average velocity over the interval t= (0.99, 1.01) you will get a very good approximation of the actual velocity at t=1.
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    Re: Find the Average Velocity

    Thank you ebaines for the detailed explanation. Yes, I know how to find the slope using the Derivative.

    When I find the derivative of 4t^2 + 3t, I get 8t + 3.

    If my calculations went correctly, the Velocity at t = 1, might be 8(1) + 3 = 11.
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  6. #6
    MHF Contributor ebaines's Avatar
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    Re: Find the Average Velocity

    Correct!
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