Shooting an object in motion really isn’t too difficult. Best practice is to move with it. Keeping with the spirit of the challenge let’s go over different types of moving shots.
A trucking shot is when the object and capture device are both in motion. Most often it’s when you’re “trucking” along side a moving object. Most likely moving at the same speed. Overall the benefit of this is you are more likely to getting better focus and a crisper subject.
A tracking shot is when you are following the movement of an object from a stationary position. Focus can be a bit harder to pull but can yield interesting results.
In camera movement is also a type of moving shot, but tend not to show up as much in photography. They are typically a video thing. An in camera move is accomplished by changing your focal length or zooming in/out for an object. I couldn't find a compelling example of a change in focal length.