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Math Help - Is this equation Correct and can it be simplified/ solved for Vmax

  1. #1
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    Is this equation Correct and can it be simplified/ solved for Vmax

    Good day to you all,

    I have the following fixed values: -
    Acceleration = 1000 mm/s2 - (Aa)
    Deceleration = -400 mm/s2 - (Ad)
    Total Distance = 450 mm - (St)
    Time is totally variable/infinite and not a factor


    The object starts from velocity(u1) and accelerates a distance (Sa)to reach a velocity of Vm.
    It then decelerates from velocity Vm a distance (Sd)to final velocity (V2).
    Distance Sa and Sd have to total the full distance travelled - St

    I would like to know the maximum velocity reached by the object.
    From this I can the easily calculate the distance Sa and Sd.

    Now I believe that..........
    S_a = (V_m^2 - U_1^2)/(2*A_a)

    And obviously
    S_d = (V_2^2 - V_m^2)/(2*A_d)

    So if acceleration distance S_a = S_t - S_d

    Then we can substitute Sa in above to get: - S_t - S_d = (V_m^2 - U_1^2)/(2*A_a)
    So
     S_d  = S_t + (V_m^2 - U_1^2)/(2*A_a)

    Combining gives us
    S_d = (V_2^2 - V_m^2)/(2*A_d) = S_t + (V_m^2 - U_1^2)/(2*A_a)


    I have tried multiply out and simplifying and in all honesty disappeared up .......

    If I am right on the track, and that would be great!
    Can one of you gurus simplify it and solve for Vm for two states: -

    1. Values of starting velocity U1 and finishing velocity V2 both are 0
    2. Given any starting velocity U1 and finishing velocity V2 if that's possible

    Thank you so much
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  2. #2
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    Re: Is this equation Correct and can it be simplified/ solved for Vmax

    This line
    Quote Originally Posted by calltronics View Post
    So
     S_d  = S_t + (V_m^2 - U_1^2)/(2*A_a)
    Should be
     S_d  = S_t - (V_m^2 - U_1^2)/(2*A_a)

    That's all
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  3. #3
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    Re: Is this equation Correct and can it be simplified/ solved for Vmax

    you sure?
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  4. #4
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    Re: Is this equation Correct and can it be simplified/ solved for Vmax

    You had
    S_a=S_t-S_d

    So
    S_d=S_t-S_a

     S_d  = S_t - (V_m^2 - U_1^2)/(2*A_a)
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  5. #5
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    Re: Is this equation Correct and can it be simplified/ solved for Vmax

    Dam, never doubted you!
    That is why it never calculate out properly!
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  6. #6
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    Re: Is this equation Correct and can it be simplified/ solved for Vmax

    So the question now is........
    Can anyone rearrange this lot to solve Vm


    1. When V2 and U1 = 0
    2. Arbitrary values of V2 and U1



     (V_2^2 - V_m^2)/(2*A_d) = S_t - (V_m^2 - U_1^2)/(2*A_a)
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