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Need help in derivation

  1. Oct 15, 2004 #1

    I'm new to the forums. This is my first thread here. I just wanted help in knowing where the motion equations (s=ut+0.5at^2, and v^2=u^2+2as) are derived from?

    Thanks in advance..
  2. jcsd
  3. Oct 15, 2004 #2


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    They are a consequence of the definition of acceleration as the second derivative of position (as a function of time). When the acceleration is constant, it's easy to find the velocity by doing a very simple integration.



    The constant term is the velocity at time t=0. If we integrate this, we find the position as a function of time.


    I could have added a new constant term that would have represented the position at time t=0, but this is usually chosen to be zero.

    The second equation in your post can be derived from the velocity and position equations above.
  4. Oct 16, 2004 #3
    fundamentally they were derived from equation of acceleration.

  5. Oct 17, 2004 #4
    start off with the definition of acceleration...
    [tex]a = \frac{v_f-v_0}{t}[/tex]
    [tex]v_f = v_0 + at[/tex]

    Definition of average velocity...
    [tex]v_{ave} = d/t[/tex]
    [tex]d = \frac{v_f + v_0}{2}t[/tex]


    [tex]d = \frac{(v_0+at) + v_0}{2}t[/tex]
    [tex]d = \frac{2v_0 + at}{2}t[/tex]
    [tex]d = v_0t + \frac{1}{2}at^2[/tex]

    For the second equation...it just a lot of manipulation of the equation above and a substitution of the definition of accleration.
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