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Laws of Motion: Force

  1. Dec 13, 2004 #1
    A time-dependent force, F=(8i-4tj) N, where t is in seconds is exerted on a 2 kg object initially at rest. At what time will the object be moving with a speed of 15 m/s?
     
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  3. Dec 13, 2004 #2

    Pyrrhus

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    Use Newton's 2nd Law rearranged in this way:

    [tex] \sum_{i=1}^{n} F_{i} = m \frac{dv}{dt} [/tex]

    [tex] \sum_{i=1}^{n} F_{i}dt = mdv [/tex]
     
  4. Dec 13, 2004 #3
    With this problem I figured the Acceleration = Force/Mass = 4i - 2tj. I tried using the equation velocity = at; 15=4i - 2tj which gives me a false answer and is where I am stuck at. Thanks.
     
  5. Dec 13, 2004 #4

    Pyrrhus

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    Integrate

    [itex] v_{o} = 0 [/itex]

    [tex] \int_{0}^{t} 8 \hat{i} - 4t \hat{j} dt = \int_{0}^{v} m dv [/tex]

    Note: Are you on a calculus based course?
     
  6. Dec 13, 2004 #5
    Yes, a calculus based engineering course.
     
    Last edited: Dec 13, 2004
  7. Dec 13, 2004 #6

    Pyrrhus

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    Well, then integrate then substitute for v the value 15 m/s and solve the problem.
     
  8. Dec 13, 2004 #7
    I am still having problems with this problem; I have a quadratic equation of 15^2=16t^2+4t^4, with the time equal to 2.4, but this is not the correct answer, please help, thanks!
     
  9. Dec 13, 2004 #8

    Pyrrhus

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    That's the answer around 2.4 seconds.
     
  10. Dec 13, 2004 #9
    Thank you!
     
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