Average Velocity & Instantaneous Velocity...5

Discussion in 'Calculus' started by nycmathguy, Mar 27, 2022.

  1. nycmathguy

    nycmathguy

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    Calculus 1
    Extra question not from Chapter 1.

    Given the position function s(t) = 2t^3 - 2t^2, where s is in meters and t in seconds, find

    A. Average Velocity from t = 1 to t = 3
    B. Instantaneous Velocity at t = 4

    Part A

    2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

    2(1)^3 - 2(1)^2 = 2(1) - 2(1) = 2 - 2 = 0

    Let A_v = average velocity

    A_v = (36 - 0)/(2 - 1)

    A_v = 36/1 = 36

    A_v = 36 m/t

    Part B

    Let s'(t) = instantaneous velocity

    s'(t) = 6t^2 - 4t

    Let t = 4

    s'(1) = 6(4)^2 - 4(4)

    s'(1) = 6(4) - 4

    s'(1) = 24 - 16

    s'(1) = 8 m/t

    You say?
     
    nycmathguy, Mar 27, 2022
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  2. nycmathguy

    MathLover1

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    correct
     
    MathLover1, Mar 27, 2022
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    Very good. This is it for today. My weekend is almost over. It's insane how quickly Saturday and Sunday go by.
     
    nycmathguy, Mar 27, 2022
    #3
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