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I have attached an image showing the three possible solutions (as determined by Mathematica) when solving for the peak velocity(Vs) in a trapezoidal move where the following are already known: distance(d),total time(t),units of acceleration(Ma),units of deceleration(Ma),initial velocity(Vi), final velocity(always zero for my purposes).

One of these equations is presumably correct, and you will notice that the second two equations contain an imaginary number 'i" in two places in the equation. I am trying to write the correct equation up in a programing language that has no provision for incorporating imaginary numbers.

Is there a way I can rewrite these equations without the 'i' imaginary number... substituting the 'i' with a placeholder of some kind and changing the negative values that need to be "square rooted" with positive ones?

I already tried writing up the first equation which uses no 'i' imaginary numbers in the programming language but the value under the square root turns out to be a negative number, causing an illegal square root error. If I simply change the value to positive the equation will process but it does not give a true answer based on the known values I input. I'm guessing that this is not the equation that will give me the actual solution, so I will need to use one of the two equations that involve imaginary numbers.

Can anyone help?

Thanks

One of these equations is presumably correct, and you will notice that the second two equations contain an imaginary number 'i" in two places in the equation. I am trying to write the correct equation up in a programing language that has no provision for incorporating imaginary numbers.

Is there a way I can rewrite these equations without the 'i' imaginary number... substituting the 'i' with a placeholder of some kind and changing the negative values that need to be "square rooted" with positive ones?

I already tried writing up the first equation which uses no 'i' imaginary numbers in the programming language but the value under the square root turns out to be a negative number, causing an illegal square root error. If I simply change the value to positive the equation will process but it does not give a true answer based on the known values I input. I'm guessing that this is not the equation that will give me the actual solution, so I will need to use one of the two equations that involve imaginary numbers.

Can anyone help?

Thanks