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Math Help - Kinematics (Complex)

  1. #1
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    Kinematics (Complex)

    Question:
    A particle moves on the positive x-axis. The particle is moving towards the origin O when it passes through the point A, where x=2a, with speed \sqrt{\left(\frac{k}{a}\right)}, where k is constant. Given that the particle experiences an acceleration \frac{k}{2x^2} + \frac{k}{4a^2} in a direction away from O, show that it come instantaneously to rest at a point B, where x=a. Immediately the particle reaches B the acceleration changes to \frac{k}{2x^2} - \frac{k}{4a^2} in a direction away from O. Show that the particle next comes instantaneously to rest at A.

    My Problem with this question:
    I have no idea on how to approach it. Please help. Thanks in advance.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Air View Post
    Question:
    A particle moves on the positive x-axis. The particle is moving towards the origin O when it passes through the point A, where x=2a, with speed \sqrt{\left(\frac{k}{a}\right)}, where k is constant. Given that the particle experiences an acceleration \frac{k}{2x^2} + \frac{k}{4a^2} in a direction away from O, show that it come instantaneously to rest at a point B, where x=a. Immediately the particle reaches B the acceleration changes to \frac{k}{2x^2} - \frac{k}{4a^2} in a direction away from O. Show that the particle next comes instantaneously to rest at A.

    My Problem with this question:
    I have no idea on how to approach it. Please help. Thanks in advance.
    HAve you tried taking the derivative and realizing that there is a max or min when v(t)=0?
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