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Math Help - Converting Accelleration to Velocity

  1. #1
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    Converting Accelleration to Velocity

    I need to convert accelleration to velocity.

    With an accelleration of 1.32944 x 10^(-7) m/s^2, and an innitial velocity of 0 m/s, to find the velocity, I would need to find the square root of the accelleration, then multiply by the time at that velocity, correct?
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    Super Member Aryth's Avatar
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    Quote Originally Posted by Thrawn View Post
    I need to convert accelleration to velocity.

    With an accelleration of 1.32944 x 10^(-7) m/s^2, and an innitial velocity of 0 m/s, to find the velocity, I would need to find the square root of the accelleration, then multiply by the time at that velocity, correct?
    The accelration formula is this:

    a = (v_f - v_0)/t

    You can rewrite it to look like this:

    v_f = v_0 + at

    v_f = (1.32944 x 10^(-7))t

    All you need is JUST the time, you don't need to find the square root of anything.

    To prove it can actually be written that way is this:

    You have a position-time function x(t):

    x(t) = x_0 + v_0t + 1/2at^2

    We know that the derivative of x(t) = v(t) or a velocity-time function

    The derivative of the constant x_0 = 0
    The derivative of v_0t = v_0 because the derivative of t^n = nt^n-1, so if v_0t then 1 * v_0 = 1v_0 = v_0 and t^(1-1) = t^0 = 1: v_0 * 1 = v_0
    The derivative of 1/2at^2 = at because the derivative of t^n = nt^n-1, so if 1/2at^2 then 2 * 1/2a = 1a = a and t^(2-1) = t^1 = t: a * t = at

    v(t) = v_0 + at

    Thus proving our formula is correct where v(t) = v_f

    Another way is to take the given acceleration formula:

    a = (v_f - v_0)/t

    multiply by t on both sides:

    at = v_f - v_0

    Add v_0 to both sides:

    at + v_0 = v_f

    This ALSO proves the formula above.

    There are no radicals involved in this.
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    What would I need to do if I don't know the time?
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  4. #4
    Super Member Aryth's Avatar
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    Quote Originally Posted by Thrawn View Post
    What would I need to do if I don't know the time?
    You could use this:

    x = x_0 + v_0t + 1/2 at^2

    total distance traveled = (initial position) + 1/2 (1.32944 x 10^(-7))t^2

    Solve for t if you know the initial position and total distance traveled, one of these is most likely zero.
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