The speedometer bounces and the car jerks

scan for codes first and check fuel pressure with a gauge auto parts rent it.

To me it sounds like you have a bad VSS, (vehicle-speed sensor)when this sensor goes out it will cause the issue you have described, here is the location of the sensor and how to change it out. They call it an out shaft speed sensor which is the same thing. Check out the images (below). Let us know what you find.