Let's assume i got this body (red one) wich is moving along the x-axis. It has got two forces on it, one called $F$, which is constant, and the other called $D$ which is the drag caused by the air that will vary. Could i describe its movement with these equations and using small intervals of time, for example: $t=0.001\ \rm s$ Getting the acceleration with Newton's Second Law where $F$ is constant and $D$, which is drag, will vary depending the velocity.
Equation to calculate drag. Here i assume $\rho$, $Cd$, and $A$ to be constant. $$D=0.5\rho* Cd * A *v^2$$ Equation to calculate velocity. $$v=v_o+at$$
Equation to calculate position. $$x=x_0+v_0t+0.5at^2$$
Assuming everything said let's go for and example. We have that: $$F=100\ \rm N$$ $$v_0=0 \ \rm m/s$$
I first calculate the $a$ (acceleration) assuming that $D$ is $0$ beacuse $v_0 = 0\ \rm m/s$. When we got $a$ we use it with the velocity equation to get the velocity. Then we use all the variables in the position equation to get the position. Then, with the velocity we have calcualted we get the drag force and then we get a different acceleration which i will use to calculate another time the $v$ and $x$, and the i would continue doing the same thing with these intervals of $t=0.001\ \rm s$. I have computed that and i finally get a constant velocity, which i supose it is the "terminal velocity".
Can this be done this way?