I never said an elephant was slower than a human. Even a poodle can run faster than a human. But an elephant is slow in comparison to the length of its legs, and an animal that heavy wouldn't make much of a predator if it can't even jump over a small obstacle. So if T-Rex weighed the same as an elephant, it probably lumbered around. T-Rex has the added disadvantage of only 2 legs, where 4 legs are always better for speed, all else being equal. The fastest 2 legged animal is an ostrich, but it has very long legs and only weighs around 300 lbs. It is built for speed, imagine how fast it would be if it had 4 legs.
If T-Rex was a predator, its prey must have been very sluggish. It could also have been a scavenger, egg eater, fisher, ambush hunter, or some combination. We'll probably never know, but don't tell that to the people who make documentaries.
ra