The Kernel Panic mentions possible bad memory. I would try re-seating the memory or at least make sure both memory modules are locked into place by pressing on each one.
If this doesn't help, then the memory slot nearest the Bottom Case may be bad. Overtime the solder joints on the memory slot nearest the Bottom Case can become cracked and give intermittent memory errors. Pressing on the center of the Bottom Case will usually make the laptop freeze if the solder joints are bad. Removing the memory from this slot would be my next recommendation. Make sure to double check that the memory in the remaining slot nearest the Keyboard is still firmly latched in place after you remove the other module.
If you still have a problem, then remove the other module and install the first module into the slot nearest the Keyboard.
You can run a memory test by creating a bootable Memtest86 USB drive using Etcher (Mac/Windows/Linux). Option Boot the Memtest86 USB drive and select the orange icon labeled "EFI". It is very likely the "Hammer" test or "Row Hammer" test will fail, but this doesn't necessarily mean the memory is bad.
When removing the Bottom Case from the white uni-body MacBook be very careful not to pull on the rubber coating. This rubber coating can easily come off while trying to remove the Bottom Case (or even holding the Bottom Case) and there is no way to re-attach the rubber coating.
Also make sure to disconnect the power adapter and disconnect the battery before inserting or removing the memory or you will cause damage to the laptop.
Edit: For older laptops you need to run the Apple Hardware Test instead:
https://support.apple.com/kb/HT201257
