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).(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Imaginary numbers what to do with them

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