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Math Help - How to describe This as an expression?

  1. #1
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    How to describe This as an expression?

    Hi
    I have an Object which is moved by the Wind, in a special kind of way ( described below ).
    ( decimal values and pixels are allowed )

    ...
    - WindPower, is a constant value

    Every second:
    - WindVelocity is increased by WindPower
    - Object is moved 'WindVelocity number of pixels'

    How do i describe the Objects movement in pixels as an expression?
    Im not entirely sure, but i think this is close:

    ( ( T * ( T + 1 ) * ( T + 2 ) ) / 6 ) * WindPower

    ( Im sorry about the Title, but i dont know how to descibe it in a better way )
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  2. #2
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    Re: How to describe This as an expression?

    If v is the initial velocity (which is increased after the first step), then in t steps the object moves v + (v + p) + (v + 2p) + ... + (v + (t - 1)p) pixels. This is the sum of an arithmetic progression, and it equals (t/2)(2v + (t-1)p). If the initial velocity is increased before the first step, then the number is (v + p) + (v + 2p) + ... + (v + tp) = (t/2)(2v + + (t+1)p).
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  3. #3
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    Re: How to describe This as an expression?

    Hmmm

    ...
    EXAMPLE ( all values are potential floats )

    T = Time/ Seconds
    WP = 0.5

    Every second ( in this exact order ):
    - Object moves WV number of pixels
    - WV increases by WP

    Expression defining Objects movement???

    SIMULATION

    T = 0
    Object Move Total = 0
    WV = 0

    T = 1
    Object Move Total = 0
    WV = 0.5

    T = 2
    Object Move Total = 0.5
    WV = 1

    T = 3
    Object Move Total = 1.5
    WV = 1.5 ( Objcts total movement after 3 seconds )

    SOLUTION A
    ( ( T * ( T + 1 ) * ( T + 2 ) ) / 6 ) * 0.5

    ( ( 3 * ( 3 + 1 ) * ( 3 + 2 ) ) / 6 ) * 0.5

    ( ( 3 * 4 * 5 ) / 6 ) * 0.5

    ( 60 / 6 ) * 0.5

    10 * 0.5

    Total Movement after 3 Seconds = 5

    No, that expression doesnt seem to be correct...

    SOLUTION B
    (t/2)(2v + (t-1)p)

    What is 'p' supposed to represent here?
    Initial Velocity of the Object, for the purpose of this expression, is 0.
    The expression is solely suppose to reflect how Wind moves the Object, based on Time i guess.
    Last edited by CakeSpear; May 12th 2013 at 05:02 AM.
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  4. #4
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    Re: How to describe This as an expression?

    SOLUTION B

    (t/2)(2v + (t-1)p)

    Sweet, this seems to work
    There is no Initial Velocity ( 0 ), so its written simpler like this:

    (t/2)(t-1)p

    PROOF
    ( p = WindPower )
    p = 0.5


    (t/2)(t-1)p

    ( 3 / 2 ) * ( 3 - 1 ) *0,5

    1.5 * 2 *0,5

    1.5

    ...
    Thanks again Emakarov!
    Thanks from emakarov
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