The speed limit is the maximum speed allowed under optimal conditions. Conditions could warrant that you should not be doing the "limit" could be many things like the weather, traffic, conditions, etc.
Traveling at the speed limit is not a defense for running an intersection and not being able to stop. You are stating you are driving too fast for conditions if you state you can't stop.
Again, go fight it in court. Memorize the statements I listed above. You are showing no fault and you will have a defense.