Materials needed for a GPS speed switch

Hi!
I'm new to Arduino so I hope someone can help me understand what materials I need (arduino board, etc.) for a project I want to do.

What I want to do is create a switch on my motorcycle that automatically turns on or off depending on my speed. Ex. if I'm going over 20 mph I want it to be on and off at less than 20 mph.

So far I think I can use a gps for the speed input.

What I need to know is what hardware I would need and how that hardware would be set up.
Can the arduino be powered by my motorcycle battery/charging system? (12v/14v)
How can I connect the 12v accessory to the arduino to respond to the switch?
Can this even be done?

Thank you in advance for your response!

It is certainly possible to program the Arduino to read the GPS output and determine your speed, if the GPS unit has a clear view of the sky.

How the Arduino would control a 12 volt device depends on the device, so you'll need to provide more information.