Even if we can't observe how fast dinosaurs ran in real life (at least for now), there's nothing that says we can't do our damnedest to figure it out experimentally. After all, if dinosaurs do make their big comeback, questions like "how fast do they run?" and "wait a minute...how fast can I run?" are precisely what you'll want answered.
That's why researchers William Sellers and Phillip Manning—paleontologists from the University of Manchester—used a computer program called GaitSym to model the top speed of five different dinosaurs: Compsognathus, Velociraptor, Dilophosaurus, Allosaurus and T. rex. (All of which, it bears mentioning, were bipedal and carnivorous.)
The pair used data from known fossil models to reconstruct the dinosaurs' locomotive anatomies and musculoskeletal features. These models were then pushed to their limits in the GaitSym program, which ran each dinosaur's model through different combinations of "muscle activation patterns." Those patterns that caused the models to falter were abandoned, while simulations where the dinosaur ran at least 15 meters were investigated more thoroughly. The researchers then proceeded to compare each dinosaur's best running speed with that of a modern-day, non-extinct equivalent.
Finally, Sellers and Manning simulated the running speeds of humans, emu and ostrich as points of anatomical and top-speed reference. Here are the figures they came up with, as reported in Proceedings of the Royal Society B (chart via).
The upshot? The smaller the dinosaur, the faster it runs (at least for these bipedal beasties). The good news is that according to Sellers and Manning's models, the monstrous T. rex would actually be the easiest of the simulated dinosaurs to outpace in a sprint for your life. The bad news? Considering the average T. rex clocked in at about .44 kilometers per hour faster than the average human, there's still a pretty good chance you're humped. (Even with a head start, Usain Bolt—who holds the world record for top speed by a human at 36 km/h—would eventually be overtaken by a Dilophosaurus).
I suppose the only consolation hidden in these findings is that when Sellers and Manning performed these simulations in 2007, they were still using model predictions that put T. rex's weight at 6,000 kg, but a recent study published in PLoS put this figure at over 8,000 kg. So by extending the rough pattern of bigger=slower, the newer, larger T. Rex model would lag just a bit behind your average human.