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Math Help - Finding final 'X Velocity'

  1. #1
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    Finding final 'X Velocity'

    Hi
    I have never been very good with advanced math, and i dont even know if this is the correct area to ask this kind of question.
    But anyway here goes:

    ...
    I have a Ball and i want to determine its final X Velocity after X seconds

    Lets say the Ball has no initial X Velocity and starts at coordiantes 0,0.
    Lets say the Balls X Acceleration ( Wind Acceleration ) is increased by 1 every second.
    Lets say the totall flight time of the Ball is 6 seconds ( this is variable ):

    BALLS X ACCELERATION ( for each second )
    1, 2, 3, 4, 5, 6

    BALLS X VELOCITY ( for each second )
    1, 3, 6, 10, 15, 21

    ...
    The data i am interested in retrieving is the Balls final X Velocity 21, but i want a formula wich automatically determines this final X Velocity based on X Acceleration ( in this case, 1 ) and Flight Time ( in this case, 6 Frames ).
    I have tried for a long time to figure this out but have not make any headway yet.
    Any help as to how i can find Final X Velocity would be much appreciated
    Thanks
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  2. #2
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    Re: Finding final 'X Velocity'

    your table values for velocity are incorrect based on the way you have defined acceleration ...

    for t in seconds ...

    a = t

    v = v_0 + \frac{t^2}{2} , where v_0 is the velocity at time t = 0
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    Re: Finding final 'X Velocity'

    Thanks for the reply Skeeter!
    Although i fail to see how that simple formula can yield the number 21 in the above example

    Asi said, ive never been particularly good at this stuff.
    I might be using the wrong terms or something, but regardless the data i have listed above is correct.

    ...
    Let me clarefy.
    This is what happens every second in the exact order:

    - Wind Power is increased by 1 ( meters per second )
    - Wind Power is added to the Balls X Velocity ( meters moved per second )
    - Balls position is moved 'X Velocity' number of meters to the right

    After X number of seconds, i want to know what the X Velocity of the Ball is.

    ...
    As i already said i might be using wrong terms or words, so feel free to correct me so i wont make the mistake in the future.
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  4. #4
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    Re: Finding final 'X Velocity'

    Quote Originally Posted by CakeSpear View Post
    Although i fail to see how that simple formula can yield the number 21 in the above example

    as I said ... your given acceleration will not yield the values you have for velocity

    Asi said, ive never been particularly good at this stuff.
    I might be using the wrong terms or something, but regardless the data i have listed above is correct.

    ...
    Let me clarefy.
    This is what happens every second in the exact order:

    - Wind Power is increased by 1 ( meters per second )
    - Wind Power is added to the Balls X Velocity ( meters moved per second )
    - Balls position is moved 'X Velocity' number of meters to the right

    After X number of seconds, i want to know what the X Velocity of the Ball is.

    ...
    As i already said i might be using wrong terms or words, so feel free to correct me so i wont make the mistake in the future.
    if you wish to have the velocity ...

    v = 1, 3, 6, 10, 15, 21 for t = 1 , 2 , 3 , 4 , 5 , and 6

    the velocity would be v = \frac{t(t+1)}{2}

    and the acceleration would be a = t + \frac{1}{2}
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  5. #5
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    Re: Finding final 'X Velocity'

    Thanks again Skeeter!
    That formula works mint for the example i gave!

    I however forgot to mention that the Wind Power need to be variable ( any Decimal or Integer ).
    Say if i change the Wind Power to 2 ( or any other number ) for example:

    v = 2, 6, 12, 20, 30, 42

    The above formula fails to produce correct results.
    Thanks again
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    Re: Finding final 'X Velocity'

    Quote Originally Posted by CakeSpear View Post
    Thanks again Skeeter!
    That formula works mint for the example i gave!

    I however forgot to mention that the Wind Power need to be variable ( any Decimal or Integer ).
    Say if i change the Wind Power to 2 ( or any other number ) for example:

    v = 2, 6, 12, 20, 30, 42

    The above formula fails to produce correct results.
    Thanks again
    Understand that if you create a new function for velocity, its time rate of change (acceleration) also changes.

    now, if you want v = 2, 6, 12, 20, 30, 42 (which is double your last velocity function)

    v = t^2 + t

    a = 2t + 1

    note the acceleration also doubles.

    Understand that acceleration is the derivative (time rate of change) of velocity ... there is no getting around that.
    if you change velocity, you change the acceleration
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  7. #7
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    Re: Finding final 'X Velocity'

    Yes i understand that.
    Logicaly if an Objects Acceleration changes, its Velocity will also change.

    ...
    Let me tell you more about the background for this question:

    I have somewhat of a computer programm wich launches a Ball of a Cliff at an Angle and Speed.
    I am now trying to determine the Balls Final Xposition along Ground Level.
    I have been following this video:


    I see now that the way the video finds "Final Xposition along ground level" is:
    Final X velocity * flightTime

    Wich will not work for my situation since my Ball is affected by Winds and so Xvelocity is not constant.
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  8. #8
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    Re: Finding final 'X Velocity'

    Quote Originally Posted by CakeSpear View Post
    I see now that the way the video finds "Final Xposition along ground level" is:
    Final X velocity * flightTime

    Wich will not work for my situation since my Ball is affected by Winds and so Xvelocity is not constant.
    In general, you can find the position function by integrating the velocity function with respect to time. If we use that last equation, v=t^2+t, the position s at time t would be given by s(t) = \frac13t^3+\frac12t^2+s_0, where s_0 is the initial position.
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  9. #9
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    Re: Finding final 'X Velocity'

    Reckoner, Ill have to take some time and try to diges what you just said.

    Well in my programm i am already able to ( by help from the above video ) determine:
    - The Balls Final Y velocity ( with decimal presicion ) as it hits ground.
    - The Balls total flight time ( with decimal presicion ) before it hits ground.

    Regardless of launch Angle or Speed, before the Ball even starts moving.
    Can this help me in any way?
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