The problem with v^2 is that it has very little effect near 0, so the
object will not be properly dampened to a stop. To simulate air
resistance, you want to use a v^2 term, but to simulate damping (and get
a stable simulation) you want to use a v term. Thus, you add a force
proportional to A*v*v + B*v, where B might be in the range of 0.01 for a
timestep of 0.01, and A might be in the range 0.001 (depending on the
maximum velocity you want to achieve).
Cheers,
/ h+