2000 Ford Crown Victoria acceleration jerking

Having a problem with my crown vic. When I have been coasting roughly between 40 and 50 mph for a bit, then I lightly press on the accelerator to speed back up, the car jerks for a moment. If I start at zero and accelerate constantly up to speed there isn't a problem (no jerks). It only occurs if I am already at speed and try to accelerate lightly. It doesn't occusr if my speed is low (10s or 20s) or high (60s or 70s), it only happens in that 40-50mph middle range.

The car seems to be be shifting up and down just fine, its just the acceleration that is a problem. I read somewhere else that this could be a problem with the sensor that detects the throttle position. Does that sound plausible? I'm also wondering could this possibly be a clogged fuel injector? How much do you think repairing something like this would cost?

Thanks so much.