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Math Help - position, velocity, and acceleration problem

  1. #1
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    position, velocity, and acceleration problem

    I am reviewing for AP Calc test and I need some help b/c i don't remember how to quite do this problem.

    the position of a particle moving along a straight line is given by
    s=t^3-6t^2+12t-8
    a. the minimum value of the speed is:
    (A) 1 (B) 2 (C) 3 (D) 0 (E) none of these

    b. the speed of the particle is decreasing for:
    (A) t>2 (B) t<3 (C) all t (D) t<1 or t>2 (E) none of these
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  2. #2
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    Quote Originally Posted by yoman360 View Post
    I am reviewing for AP Calc test and I need some help b/c i don't remember how to quite do this problem.

    the position of a particle moving along a straight line is given by
    s=t^3-6t^2+12t-8
    a. the minimum value of the speed is:
    (A) 1 (B) 2 (C) 3 (D) 0 (E) none of these

    b. the speed of the particle is decreasing for:
    (A) t>2 (B) t<3 (C) all t (D) t<1 or t>2 (E) none of these
    Dear yoman360,

    First differentiate the given equation with respect to x and then factorize it. Afterwards by setting \frac{dy}{dx}=0 you could find the minimum speed. Also by considering \frac{dy}{dx} in the intervals given in part b you could find the interval at which teh particles speed is decreasing.

    Hope this will help you. If you need more help please don't hesitate to reply me.
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  3. #3
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    Quote Originally Posted by yoman360 View Post
    I am reviewing for AP Calc test and I need some help b/c i don't remember how to quite do this problem.

    the position of a particle moving along a straight line is given by
    s=t^3-6t^2+12t-8
    a. the minimum value of the speed is:
    (A) 1 (B) 2 (C) 3 (D) 0 (E) none of these

    b. the speed of the particle is decreasing for:
    (A) t>2 (B) t<3 (C) all t (D) t<1 or t>2 (E) none of these
    The velocity is the derivative of the position function. Since the position function is cubic, the velocity is a quadratic function of the time. Completing the square in that quadratic will answer all of these questions.
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  4. #4
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    thanks
    for
    a. I got (D) 0 minimum at t=2 plug 2 into velocity function and got 0
    b. i got (E) none of these because the speed is always positive except for t=2 where speed is 0.

    CORRECT?
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  5. #5
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    Quote Originally Posted by yoman360 View Post
    thanks
    for
    a. I got (D) 0 minimum at t=2 plug 2 into velocity function and got 0
    b. i got (E) none of these because the speed is always positive except for t=2 where speed is 0.

    CORRECT?
    Dear yoman360,

    Yes you are correct. Hope you have understood the concepts well.

    Goodbye!!
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