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Math Help - Kinematics Aplication problem - variable acceleration.

  1. #1
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    Kinematics Aplication problem - variable acceleration.

    Hi I need help with this problem.

    A bullet is fired into a sandbag. The acceleration of the bullet within sandbag is
    -40√v, where v is velocity in ft/sec. When will the bullet stop if it enters the sandbag at 950 ft/sec.

    Than you.
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  2. #2
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    Quote Originally Posted by ado061 View Post
    Hi I need help with this problem.

    A bullet is fired into a sandbag. The acceleration of the bullet within sandbag is
    -40√v, where v is velocity in ft/sec. When will the bullet stop if it enters the sandbag at 950 ft/sec.

    Than you.
    Start by setting up an appropriate differential equation. Can you do that?
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Start by setting up an appropriate differential equation. Can you do that?
    I am trying to work with m(dv/dt)=F-kv

    dv/dt=950-40v^1/2

    Now I can solve this by separation of variables.
    Does this make sense.
    Thanks
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  4. #4
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    Quote Originally Posted by ado061 View Post
    A bullet is fired into a sandbag. The acceleration of the bullet within sandbag is
    -40√v, where v is velocity in ft/sec.
    When will the bullet stop if it enters the sandbag at 950 ft/sec.
    *** \displaystyle \frac{dv}{dt} = -40\sqrt{v}

    separate variables and solve for velocity as a function of time
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  5. #5
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    Quote Originally Posted by skeeter View Post
    *** \displaystyle \frac{dv}{dt} = -40\sqrt{v}

    separate variables and solve for velocity as a function of time
    Thank you, I got it now.
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