What's the problem when your car jerks and speedometer goes up and down

Hello, if your speedometer is moving erratically even when not moving, you clearly have some kind of electrical circuit issue. You could have a problem with the speed sensor that provides information to the speedometer -- either with the sensor, the driven gear, or the wiring or connector to the system. A good diagnostic tool should be able to monitor sensor output and test the system. You could also have some kind of other issue with power or ground, or even a vehicle charging system issue causing display issues.