I hope you can follow my train of thought (I'm not being elitist here, I am open to the possibility that my post may be unintelligible) 1. Velocity is a parallel rate. The distance/time formula with which we are familiar is an expression of the number of meters laid end to end alongside one second. For example, another parallel rate would be the number of traffic signs alongside a kilometer of roadway. 2. Parallel rates have reversible numerators and denominators. 1 meter per second is the same as 1 second per meter. Looking back at my example of the roadway, we can see that 4 signs per kilometer is the same as .25 kilometers per sign. So the fundamental issue of velocity is how we address the inevitable increase of one component with respect to the other. Imagine that an object's velocity increases from 1 m/s to 2 m/s. All of a sudden there is twice as much distance alongside the same 1 second of time. Was this accomplished by the squeezing of 2 meters into one second? Or was it accomplished by the stretching of that second out to a distance of 2 meters?