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Find the power of a boat that accelerated

  1. Oct 13, 2011 #1
    A 3.5x107 kg ship is travelling at 7 m/s. The ship is accelerated forward with a F of 4.5 x 105 N over a distance of 2 km.

    What is the final speed? Vf = 10 m/s

    How long does it take the ship to traverse the 2 km? T = 233.33 seconds

    What is the average power which the engines had to produce to accelerate the ship in part 1? I need help on this please.

    You can do P = W/t = (4.5x105 x 2000) / 233.333

    P = 3.9 x 106 watts which is the right answer.

    However, how come you can't do P = (F)(avg velocity)

    P = 4.5x105 * (3/2) = 675000 watts??
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 13, 2011 #2

    cepheid

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    Hi,

    Where'd you get your avg velocity from?

    You can use this formula, and in fact the two methods are equivalent, since:

    P = W/t = Fd/t = F(d/t) = Fvavg

    vavg = d/t = 2000 m / 233.33 s = 8.57 m/s

    4.5e5 N * 8.57 m/s = 3.9e6 Nm/s (= J/s = W)
     
  4. Oct 13, 2011 #3

    cepheid

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    Ah I see. It looks like you were confused in your formula for avg. velocity. It's (vf + vi)/2 NOT (vf - vi)/2.

    (10 m/s + 7 m/s)/2 = 17/2 m/s = 8.5 m/s
     
  5. Oct 14, 2011 #4

    Oh my goodness!!! Your eyes are so good!!!! I have been using energy formulas all day that do Xf-Xi all day!! Such a silly mistake thank you so much!!! it is so late and my brain if frazzled :)
     
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