Question about fiding speed and distance

  1. I had a test earlier today and one question was,

    A 20kg object initially at rest is accelerated at constant power of 12.0w. After 9.0s it has moved 56.0m. Find its speed at t=6.0s and its position at that instant.

    I got v=6 and distance=36m are these values correct?
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,683
    Staff Emeritus
    Science Advisor

    I started to say that this makes no sense. An object accelerates at a constant acceleration measured in [itex]m/s^2[/itex]. That acceleration may be caused by a constant force, measured in Newtons, but not a constant power measured in watts.

    But the "12.0 w" really has nothing to do with the problem and can be ignored. If an object accelerates from rest at constant acceleration, a [itex]m/s^2[/itex], then after time, t, it will have speed [itex]at[/itex] m/s and will have moved distance [itex](1/)at^2[/itex] m.

    They do not look at all right to me. How did you get them?
     
  4. P*t=W
    12*9=108
    therefore W=108joules
    W=F*displacement
    F=108/56
    F=1.93N

    F=ma
    a=1.93/20
    a=0.1

    so at t=6
    Pt=W
    12*6=72joules
    W=72joules

    W=F*displacement
    displacement=72/(20*0.1)
    displacement=36m

    P=Fv
    v=12/(20*0.1)
    v=6
     
  5. russ_watters

    Staff: Mentor

    Halls, it doesn't say constant acceleration. Constant power is what you might get from a car with a continuously variable transmission.
     
  6. I am assuming the acceleration is constant. Is that right?
     
  7. Have I gone wrong somewhere?
     
  8. This is the question given in the test word for word. The question confused me for ages, in the end I just assumed acceleration was constant. I don't know how you could work it out any other way.
     
  9. adjacent

    adjacent 1,533
    Gold Member

    Try not to round of numbers.Use fractions.
     
  10. Acceleration can not be constant...
    P=dW/dt
    P=d(∫F.dx)/dt
    P=F.dx/dt
    P=Fv
    If a is const.
    P=ma*(at)
    P=ma2t
    Then Power is not constant as given in the question...
     
  11. f95toli

    f95toli 2,414
    Science Advisor
    Gold Member

    I saw this question when it was in the other section, it looked fishy to me then and I just had a go at it. Unless I am missing something it does not have a solution.
    The way the question is formulated you will -as Enigman pointed out- end up with a 2nd order ODE for the position; but then the constants are over-determined.

    I wonder if this is a case of the teacher trying to add a red herring (constant power) without realizing that this implies that the accelaration can not be constant.
     
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