I'm interested in simulating the (one-dimensional) speed and position of a car.
How can I compute the speed $v(t)$ given initial speed $v_0$, acceleration $a(t)$ (I don't want to assume that it is constant) and a drag independent of the time and dependent only of the current speed in a quadratic way, i.e., $d(t) = d_0 \cdot v^2(t)$?
I'm stuck at $v(t) = \int a(t) dt$ and don't know how I can incorporate the drag.
I'm not sure I understood the question, is a(t) given?
If yes so write $ dV/dt+d_1V^2=a(t)$
now if a(t) is a constant you can separate variables and get $dV/(a(t)+d1_V^2)=dt$ and do integration from $V_0$ to V and $t=0$ to t here is the answer $V(0)=V_0, d_1=d_0/M$ M=mass of body