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Math Help - Velocity and Acceleration--Derivatives

  1. #1
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    Velocity and Acceleration--Derivatives

    Which graph has:

    (a) Constant velocity

    (b) Greatest initial velocity

    (c) Greatest average velocity

    (d) Zero average velocity

    (e) Zero acceleration

    (f) Positive acceleration throughout

    Thank you =)
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  2. #2
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    Please?
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  3. #3
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    Hello, melliep!

    Recall that: .slope = velocity.
    . . . . . . .concavity = acceleration


    Code:
        (1) |                     (2)  |          *
            |                          |
            |   *                      |         *
            |*     *                   |        *
          - * - - - * - - - * -      - + - - -*- - -
            |        *     *           |   *
            |           *              *
            |                          |
    
    
        (3) |          *           (4) |
            |      *                   *
            |   *                      | *
            | *                        |   *
            |*                         |     *
            |                          |       *
          - * - - - - - - -          - + - - - - * -
            |                          |

    Which graph has:

    (a) Constant velocity

    Constant velocity = constant slope.

    If the slope doesn't change, we have a straight line . . . graph (4)



    (b) Greatest initial velocity

    The graph with the steepest slope at t = 0 is graph (3).



    (c) Greatest average velocity

    Graph (1) has a slope that is positive sometimes, negative sometimes.
    I suspect that the average velocity is 0.

    Graph (4) has a constant negative slope.

    Graph (3) always has a positive slope, but it is decreasing.

    Graph (2) always has a positive slope and it is increasing.

    I'd bet on Graph (2).



    (d) Zero average velocity

    As I suspected, it must be graph (1).



    (e) Zero acceleration

    Zero acceleration = zero concavity.

    We must have a straight line . . . graph (4).



    (f) Positive acceleration throughout

    Positive accelration = positive concavity (concave up).

    The curve that is always concave up is graph (2).
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  4. #4
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    you are utterly amazing. thank you so much i really really appreciate it.
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