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Velocity and acceleration and drag

  1. Aug 29, 2012 #1
    This is probably a maths question which im struggling with
    the question states that
    drag is proportional to the square of the velocity
    D = kv^2

    And there is a linear relationship between the square of the velocity and the acceleration
    dv/dt = - 0.0154 v^2 + 0.402827

    assume the mass of the object is 700 kg

    F = ma
    F = 700 dv/dt
    and the force = propulsion- drag = P - D
    P - D = 700 dv/dt
    dv/ dt = ( P - D) / 700




    with this data below how do i find the drag and the propulsion

    v^2 (m/s)__________( dv/dt) , ms/s/s
    0.6241_____________0.39
    5.0176_____________0.32
    11.2225____________0.23
    16.81______________0.15
    20.7025____________0.09
    23.2324____________0.05



    I tried putting the linear equation in the Newton second law
    dv/ dt = ( P - D) / 700
    dv/dt = - 0.0154 v^2 + 0.402827
    so , ( P - D) / 700 = - 0.0154 v^2 + 0.402827
    but how do i find the P and D ?
     
  2. jcsd
  3. Aug 29, 2012 #2
    Are the tabular data simply what you can get from the linear equation? I have tried two rows, and they fit. So I think they can be ignored.

    With ( P - D) / 700 = - 0.0154 v^2 + 0.402827, what do you get by multiplying both sides by 700? What form must the drag term have? What else is there?
     
  4. Aug 29, 2012 #3
    when multiply both sides with 700 it becomes
    P-D = 281.979 - 10.78v^2
    well since D = kv^2
    it becomes

    P - kv^2 = 281.979 - 10.78v^2
     
  5. Aug 29, 2012 #4
    my teacher kept mentioning the drag is proportion to the velocity , and she told us to find the linear relationship between acceleration and the velocity, and we can find the constant of the drag. but i dont know what she meant by that
     
  6. Aug 29, 2012 #5
    The drag is proportional to the SQUARE of the velocity, at least in this problem. Using the final equation you got, can you determine P and k?
     
  7. Aug 29, 2012 #6
    i dunno how
     
  8. Aug 29, 2012 #7
    Set v = 0. What do you get?
     
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