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Math Help - velocity word problem

  1. #1
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    velocity word problem

    Assume a tomato is in frictionless free fall with a downward velocity v increasing at a constant rate g (g is the gravitational constant). Suppose that the initial velocity is v0 and find a formula for v(t) in terms of
    v0 and g.

    b) Now introduce a negative term representing air friction that is proportional to the velocity (hence of the form -kv for some constant k). Now find a formula for v(t), Show that as t grows, the velocity approaches the terminal velocity  \frac{g}{k}
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  2. #2
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    What ideas have you had so far?
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  3. #3
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    Nothing, dont know where to start, should I be using one of the kinematics formula in physics?
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  4. #4
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    In both cases, you're essentially asked to solve a first-order differential equation. What equation could you write down for part (a)?
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  5. #5
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    How is velocity related to acceleration?
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  6. #6
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     V = V_{0} + at ?
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  7. #7
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    Quote Originally Posted by Tweety View Post
     V = V_{0} + at ?
    v = v_0 + gt


    to get you started for part (b) ...

    \frac{dv}{dt} = g - kv
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  8. #8
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    I was thinking of \frac{dV}{dt}= a but for constant acceleration, that is the same thing. Of course, in this problem, a= -g.
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  9. #9
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    Quote Originally Posted by HallsofIvy View Post
    I was thinking of \frac{dV}{dt}= a but for constant acceleration, that is the same thing. Of course, in this problem, a= -g.
    I also thought that at the start, but the problem wants the effect of air resistance of the free falling "tomato" to be a negative value (-kv) ... looks like the downward direction is positive in this case.
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