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Motion problem

  1. Dec 3, 2008 #1

    Can anybody help with the following:

    A point particle moves in a plane with trajectory given by r(t) = R [θ (t)]^3/2, where R is a constant.

    The angle θ in radians increases in time according to the equation θ (t) = 1/2 α t^2,
    where α is a constant whose numerical value is α = 1 s^-2.

    a. Sketch the trajectory of the particle.
    b. Compute the time t > 0, if any, for which the radial and tangential components of the velocity of the particle coincide.
    c. Compute the time t > 0, if any, for which the acceleration of the particle is purely tangential.
    d. Compute the time t > 0, if any, for which the radial acceleration of the particle is twice its tangential acceleration.

    I really am struggling with this question. I'm not even sure about sketching the trajectory, which is usually the least I can do in these type of questions! Can anybody help and explain it in really simple terms. Thanks for any help with this.
  2. jcsd
  3. Dec 3, 2008 #2


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    Homework Helper

    What you have is an equation in polar coordinates don't you?

    And if |R| is constant, it is described how?
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