I want to simulate a simple force-acceleration (rather than impulse-velocity) physical world made up entirely of disks and I'm having an irritating problem with my physics.

When two disks collide, I can calculate the changes in velocities quite easily using conservation of momentum and conservation of energy. Since this is going to be a force-based simulation, I need to calculate the forces to apply. I thought I'd use the momentum-impulse equality:

mΔv = FΔt

Sounds simple, except I don't know what to do with time(Δt). So I guess the question boils down to this: how long does the collision take?