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Displacement, velocity, acceleration

  1. Jan 2, 2006 #1
    A particle moves along a line so that its position at any time t>0 is given by the funciton s(t) = t^3 - 8t + 1, where s is measured in feet and t is measured in seconds.
    (a) Find the displacement during the first 3 seconds.
    (b) Find the average velocity during the first 3 seconds.
    (c) Find the instantaneous velocity when t = 3.
    (d) Find the acceleration of the particle when t = 3.
    (e) At what value or values of t does the particle change direction?

    Ok, this is pretty much just to check my answers because i'm paranoid.. Here are the answers i came out with..

    (a) 4 ft
    (b) 1 ft/s
    (c) 19 ft/s
    (d) 18 ft/s^2
    (e) sqrt(8/3)s or 1.633333s

    Is this correct?

    Thanks
     
  2. jcsd
  3. Jan 2, 2006 #2

    LeonhardEuler

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    Gold Member

    Check this one again. Other than that the answers seem fine.
     
  4. Jan 2, 2006 #3
    Yea except for that one I think they're all right.
     
  5. Jan 2, 2006 #4
    let's see.. for that one i did..

    s(t) = t^3 - 8t + 1
    s(0) = 0^3 - 8(0) + 1 = 1
    s(3) = 3^3 - 8(3) + 1 = 4
    so it would be
    average velocity = change in displacement/change in time
    average velocity = (4 - 1) / (3 - 0) = 3/3 = 1 ft/s

    not sure on this? can you point me in the right direction?
     
  6. Jan 2, 2006 #5
    Ohh yea I guess you're right I just wasn't thinking right and thought that initial displacement was zero, you're doing it right.
     
  7. Jan 2, 2006 #6

    LeonhardEuler

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    Gold Member

    Uhh, yeah never mind-oops!
     
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