From a balanced, standing position people can only move about 3 feet per second. That's any adult of relatively normal height. Shorter people move slightly faster, but over the course of one step the speed difference is negligable. This speed issue is essentially a physical constant related to gravity.
We begin talking about this speed issue very early in aikido but it is a long time before students buy into the idea because we have this funny perceptual thing that happens where we pay more attention to faster moving things. So, somebody that waves their arms fast while they are stepping relatively slowly, looks like they are stepping fast. For this reason, fast punches look dangerous even though they can't land until the attacker moves his body within reach.
One thing that has really improved my perception of this fast-is-slow phenomenon is paying special attention to the two ends of the attack motion. When uke starts to move through ma-ai we have to begin our evasion - so we spend a lot of time working on paying attention to movement starting at ma-ai. The other end of the attack movement is when uke's front foot hits the ground. My instructor has recently put out a couple of excellent videotape lessons on timing based on that front foot, and we've been paying a lot more attention to that front footstrike. The combination of those two practices has really improved my perception of that time-dilation effect. It's easier for me to see for myself that fast really is slow.