Vehicle Speed Sensor fault
There are three parts of the Vehicle Speed Sensor (VSS) circuit; the VSS, the Powertrain Control Module (PCM) and the wiring between the two. The problem could be in any one, or more, of these parts.
The most likely problem would be with the VSS itself. You can check the VSS signal with a DVOM set to read AC volts. Raise the front wheels off the ground and support the vehicle with jack stands. Never, ever work on a vehicle that is supported by a jack alone. Having a vehicle fall on your chest could ruin your whole day.
Connect the leads of the DVOM to the yellow, C1-64 and purple, C1-65 wires of connector C1 (blue) of the PCM. Be very, very careful you do not damage the connections of the wires. I use a single strand of a multi-strand wire to insert into the connector then connect my leads to that. There is an electrical test kit you can buy but the single strand wire will do quite nicely in a pinch.
Put the key in the ON engine OFF position, place the transmission in DRIVE or NUETRAL and slowly rotate the right front wheel. You should get a reading of 0.4 volts AC. If the reading is good set your DVOM to ohms and measure the resistance of the whole circuit. It should read between 1650 to 3180 ohms. If not you have a problem in the wiring. If both check out good, then the problem is in the PCM.
The PCM will run about $321.45 and about an hour labor to replace and reprogram. The VSS will run about $35.17 and about a half hour to replace. Figure about one hour labor to diagnose the problem. If the problem is in the wiring; that is charged by the actual time it takes to locate and repair the problem.
The VSS is located on the end of the transmission. Remove the right front tire and you will see it. To replace it simply unplug the connector, remove the attaching bolt and remove the VSS from the transmission. Then install the new one, secure the attaching bolt and plug in the connector. Simple as that.
Read more at Suite101: Chevy Impala DTC P0502: 2001 Chevy Impala With A DTC Of P0502 http://autotechrepair.suite101.com/article.cfm/chevy_impala_dtc_p