My problem appears so simple, yet I can't find an answer:
I have an object with a certain velocity $v_0$ and acceleration $a_0$. My goal is at a time $T$ the new velocity $v_x$ and zero acceleration.
How can I calculate a function over time, that gives me the current positiv or negativ constant jerk (derivative of the acceleration) to achieve this?
The jerk (call it $j$) is the third derivative of position. Your usual equation $x(t)=x_0+v_0t+\frac 12a_0t^2$ adds a term $\frac 1{3!}j_0t^3$. You can take derivatives to give $v(t)$ and $a(t)$ then use your known points to assess the parameters. You have one too many constraints. You can compute the jerk from the difference in accelerations divided by the time, but there is no guarantee that you can meet the velocity change you want.