It probably did very little running, and when it did, it did not entirely leave the ground. It most likely achieved a "fast" walking pace.
The Speed of an animal is often determined by the scale difference between the femur and the lower leg bones. Animals with shorter femurs tend to be faster while those with longer more "human-like" leg bones are on the slow side. The T-Rex had a very large femur, nearly equal in length to it's lower leg bone. It's top speed was most likely around 17.9 mph- that's fast enough to outrun our fastest sprinters.