The very small print at the very end of the Atmel Atmega328 datasheet says that it is not suitable for automotive applications.
I'm sure that's for legal liability reasons... Almost every data sheet I've ever seen has a disclaimer that says something like, "Not for medical use". I'm sure some of these parts end-up in medical equipment and the device manufacturer takes all of the liability.
I used an Arduino for sound-activated lighting effects in my van... Not critical like a cruse control, but I'd say that's an "automotive application".
I believe most cruse controls use a [u]Servo Motor[/u]. A servo has an advantage in that the motor driver circuitry is built-in and you only have to send it a pulse-train from the Arduino to set the angle.
A stepper or even a geared-down DC motor could work, but you'd need some positional feedback (at least some limit indicators) for some throttle-position feedback (as well as the usual car-speed feedback).
...and i need a car for testing it.
I'm sure your mom won't mind if you borrow her car for some experiments.
P.S.
I had an idea once for something I never built... Something LOT easier to build than a cruse control... I was going to configure some LEDs, maybe 3 LEDs or 5 LEDs of different colors, spread-out in a row.
When you are at the "target speed", the center LED would light-up. If you go over, the LED to the right would light-up, and if you are below the target-speed, the left LED would light-up. Or maybe the LED would start to glow dimly if you get slightly off-speed.
The idea was, you can see the LEDs without directly looking at them while keeping your eyes on the road.
I had a few different ideas of how this thing was going to work. Since I never built it, I never decided what I wanted to do, but it might have one or more modes of operation...
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Like a normal cruse control. You push a button when you are at the target speed.
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Drive at a constant speed for 30 seconds or so, and the thing automatically "locks-in" the speed.
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The thing automatically locks-into the closest 5 MPH.
You might want to start with something like that before you build a full-bown speed control. If you decide to go-ahead with the cruse control, you can use the same speed sensor & Arduino and just add the servo and mechanical linkage (and brake sensor & safety features, etc.).