IP addresses can change with every session (basically when you reconnect to the internet, which is at least as often as you reboot). That doesn't mean that the address will change, but they can.
You can use the trace route command to determine who the ISP (Internet Service Provider) is for a given address, at least as long as that address is currently in use when you trace the route. Knowing this can help you, since you can then contact the administration for that provider and let them know that you're having problems with someone using their service. Given the IP address and the date and time of the problem, they can determine which of their customers was signed on using the computer.
-PatP