In this situation, the rear brake cannot contribute to stopping power, since it has no traction. If you ride a fixed gear with only a front brake, your legs will tell you exactly when you are at the maximum brake capacity of the front brake. Once your fixed gear has taught you this, you will be able to stop any bicycle better, using the front brake alone. The rear brake is O.K. for situations where traction is poor, or for when your front tire blows, but for stopping on dry pavement, the front brake all by itself provides the maximum stopping power, both in theory and in practice. If you take the time to learn to use the front brake correctly, you will be a safer cyclist.
Many cyclists shy away from using the front brake, due to fear of flying over the handlebars.
This does happen, but mainly to people who have not learned to modulate the front brake. The cyclist who relies on the rear brake for general stopping can get by until an emergency arises, and, in a panic, he or she grabs the unfamiliar front brake as well as the rear, for extra stopping power. This cannot happen when you are using only the rear brake, because as soon as the rear wheel starts to lift, there is not more braking force generated by it. Unfortunately, though, it takes twice as long to stop with the rear brake alone as with the front brake alone, so reliance on the rear brake is unsafe for cyclists who ever go fast. It is important to use your arms to brace yourself securely during hard braking, to prevent this.