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Is there some sort of calculus relationship between these two kinematics equations?

  1. Dec 25, 2012 #1
    [tex]{ y }_{ f }={ y }_{ i }+{ v }_{ yi }t+\frac { 1 }{ 2 } { a }_{ y }{ t }^{ 2 }\\ { v }_{ yf }={ v }_{ yi }+{ a }_{ y }t[/tex]

    It almost looks like the second equation is the derivative of the first equation with respect to time.
     
  2. jcsd
  3. Dec 25, 2012 #2

    Pengwuino

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    Gold Member

    Re: Is there some sort of calculus relationship between these two kinematics equation

    Exactly. The velocity of an object is simply the time-derivative of its position function.
     
  4. Dec 25, 2012 #3
    Re: Is there some sort of calculus relationship between these two kinematics equation

    Maybe I'm incredibly rusty on my calculus, but isn't the time-derivative of the first equation the following?

    [tex]0={ v }_{ yi }+{ a }_{ y }t[/tex]
     
  5. Dec 25, 2012 #4

    jtbell

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    Staff: Mentor

    Re: Is there some sort of calculus relationship between these two kinematics equation

    ##v_{yf}## isn't a constant, it's a variable, more specifically the dependent variable, a function of t. Written as functions, your two equations are

    $$y(t) = y_i + v_{yi} t + \frac{1}{2}a_y t^2 \\ v_y(t) = v_{yi} + a_y t$$
     
  6. Dec 25, 2012 #5
    Re: Is there some sort of calculus relationship between these two kinematics equation

    Thank you!
     
  7. Dec 25, 2012 #6
    Re: Is there some sort of calculus relationship between these two kinematics equation

    Any way I can derive the below equation from the position and velocity equations?

    [tex]{ { v }_{ yf } }^{ 2 }={ { v }_{ yi } }^{ 2 }+2{ a }_{ y }({ y }_{ f }-{ y }_{ i })[/tex]

    Edit: Never mind. https://www.physicsforums.com/showthread.php?t=660863
     
    Last edited: Dec 25, 2012
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