At wiki the formulas for motion are to find in chapter uniform acceleration is the formula that describes the distance of particle after a certain time with an initial speed and an acceleration.

with www.wolframalpha.com I solved the formula for the time.

the result is:

with this result I can calculate how much time a particle needs for a distance of e.g. 1mm with a initial speed and a acceleration from the field.

The acceleration of a electron in a electrical field is:

E is the field strength of the simulation [V/m] q is the elementary charge of a electron q=1.6021766208(98)×10⁻¹⁹ [A*s] and m is the mass of a electron m=9.10938356(11)×10⁻³¹ kg (link to parameter for a electron

I want still do have the same parameter for the calculation step size (s), initial speed (v) and the acceleration (a) by the field. The approach first to calculate the time ts what a particle need to travel approximately 1mm with the acceleration by the field and the previously speed. If a particle is created new in the simulation the speed is the initial speed (vxi and vyi set by user) . After the calculation of the a new position the speed is the result of the acceleration plus the previously speed. The new position of the particle is calculated with the motion formula s=a/2*ts^2+v*ts. I think by use of the common motion formula the position should be right. Even if something with the calculation of the time ts isn't right.

I think that still something is wrong as actually the yellow columns above should be equal. if I calculate the distance absS with the partly movement of the particle in x and y direction it is unequal to the distance s (1mm) what was use to calculate ts.

If somebody has a idea why have this behavior let it me know. I uploaded the with the calculation to GitHub https://github.com/Chris-deerleg/FEMM-4.2