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1d kinematics question

  1. Jan 23, 2008 #1
    1. The problem statement, all variables and given/known data

    The position of a particle moving along the x axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds.

    For the following, let the numerical values of c and b be 3.5 and 1.0 respectively.

    (b) At what time does the particle reach its maximum positive x position?

    (f) What is its acceleration at at t = 1.0 s?

    2. Relevant equations



    3. The attempt at a solution

    For (b) I tried plugging in numbers starting at 1 until the the result started to decrease. I am not sure if I must take the derivative first though.

    For (f) I am assuming you take the second derivative of the equation. Is the derivative not 2-6bt ? Answer I got : -4
     
  2. jcsd
  3. Jan 23, 2008 #2
    Well what does dx/dt represent? The rate of change.

    now I can't tell, is it sposed to be x=c*t^2-b*t^3? I'm assuming or else it's a terribly uninteresting problem

    So for b

    dx/dt=2*c*t-3*b*t^2

    you're looking for a maximum, so you set dx/dt=0 and solve for t. It's a quadratic equation so there are two solutions

    How do you decide which one's right?

    You had the right idea for f, but the second derivative is 2c-6bt=a
     
  4. Jan 23, 2008 #3

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    (Use the symbol ^ for power.)

    x = ct^2 - bt^3.

    b. At the extreme +ve posn the v would be 0, so, yes, you should find dx/dt.

    f. 2c-6bt. Now find answer.
     
  5. Jan 23, 2008 #4
    Thank you, I got (f) right. But for (b) I have another question. For the quadratic equation does c = 0? To decide which one is right, you pick the positive one because time cannot be negative. For my answer I am getting 0. This doesn't sound right.
     
  6. Jan 23, 2008 #5
    it's possible if the initial velocity is negative and it only gets more negative, then the initial position should be the biggest it ever gets
     
  7. Jan 24, 2008 #6

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    For elementary problems like these, unless otherwise mentioned, the co-efficients will not be equal to zero. But it's shows your interest that you have asked, and blochwave has given you the answer. You should then also ask what if c=0, both=0.

    Assuming non-zero b and c, have you solved it?
     
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