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Velocity Drag force and distance traveled

  1. Sep 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Microsoft-Edge-Web-Notes-Mastering61302359[2305843009214067476].jpg

    2. Relevant equations
    Sum of force

    a = dv/dt
    v = integrate a + C

    3. The attempt at a solution

    I found the equation in terms of final v, initial v... however, on the right hand side, there is another v, and I think it is time dependent, so I am not sure which value should I plug in.
     
  2. jcsd
  3. Sep 13, 2016 #2

    TSny

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    Try using the chain rule to write ##a = \frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt}##.
     
  4. Sep 13, 2016 #3
    Then do we know dv/dx and dx/dt? on the right hand side, will the velocity be initial one? thanks
     
  5. Sep 13, 2016 #4

    TSny

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    Try to express F = ma as a differential equation in terms of just the variables v and x. dv/dx is already expressed in these variables. How can you express dx/dt?

    v on the right side of a = F/m is the instantaneous velocity.
     
  6. Sep 13, 2016 #5
    so dv/dx * dx/dt = -40/m v^2 ??
     
  7. Sep 13, 2016 #6

    TSny

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    Yes. In order to get only the variables v and x to appear in the equation, what can you do with dx/dt?
     
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