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Request for equations

  1. Oct 29, 2004 #1
    Hi

    Does anyone know the projectile motion equations in which the acceleration is NOT constant?
     
  2. jcsd
  3. Oct 29, 2004 #2

    JasonRox

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    Learn Calculus.

    That's all you need.
     
  4. Oct 29, 2004 #3
    ahh.....

    Isn't there an equation(s) derived from the kinematic ones i can just apply?
     
  5. Oct 30, 2004 #4

    Integral

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    There is no way that anybody can guess what you are asking for. You will have to ask an understandable question.

    As for variable accelerations, just apply Newtons 3rd:

    F=ma
     
  6. Oct 30, 2004 #5
    I believe you probably already know the standard proceedure here, Nothing.
    Usually, beginning with F = ma,
    just take the derivative of both sides of the equation since you are looking for the time rate of change of accel.

    dF/dt = m(dA/dt)

    However, the effectiveness of this equation goes beyond the original assumptions in Newton's law. In cases of rapid change of acceleration a modification of Newton's law is probable. :surprised

    Is that what you are getting at?

    Creator
     
  7. Oct 30, 2004 #6
    F=ma is a differential equation since [itex]a =d^2 x /dt^2 [/itex] with x, a and F vectors. Given a certain force you can find the velocity or position as a function of time by integrating the force respectively one or two times. But you indeed need to know some calculus for that...
     
  8. Oct 30, 2004 #7

    Alkatran

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    Is the change in acceleration constant?

    Doesnt:
    Position = Sum(x(i)*t^i/i!)

    where i goes from 0 to infinity, x(0) is initial position, x(1) is inital speed, x(2) is inital acceleration, etc....
     
  9. Oct 30, 2004 #8
    ok u know that equation:

    y = v0 sin (theta) - 0.5at^2 ?

    where v0 sin (theta) is the vertical component the muzzle velocity

    is there a counterpart where a is not constant?
     
  10. Oct 30, 2004 #9

    arildno

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    Sure, you have:
    [tex]y(t)=v_{0}t\sin\theta-\int_{0}^{t}(\int_{0}^{\tau}a(s)ds)d\tau[/tex]
     
  11. Oct 30, 2004 #10
    thanks arildno, that really helped.
    :smile:
     
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