How is velocity involved with roller coasters?

Recall that a roller coaster is a gravity operated, fixed course, recreational vehicle. And also note that velocity is like speed, only with a direction vector associated with it. Velocity is associated with a roller coaster pretty much all along its route; it's always being acted on by gravity. The cars are acted on by another force, which is basically a "push" or "pull" with a direction vector, to increase their velocity a bit. The cars are hauled to the top of a grade, and then pushed over the top to begin their gravity-assisted acceleration. The velocity rises rapidly, and then other forces act on the cars (and the riders) as the vehicle acts on the rails and has the rails act back on them. Lots of things going on at once. Any time the cars of the ride change direction, they change velocity. They may or may not change speed, but a direction change alone is a velocity change. It's that simple. The cars are given potential energy by being lifted up the ramp. Then that potential energy is converted into kinetic energy, into motion, by gravity. (Note that some rides "throw" the car along a track to give it kinetic energy, and it coasts for the rest of the ride and is acted on by gravity and the rails. The bottom line is that any speed change or direction change must be accomplished by a force acting on the cars, and that's how velocity will change. The physics subject of mechanics deals with this pretty well, and it is fairly easy to at least qualify the things that are happening. Following qualification, which is basically stating "what" is happening, we can move on to quantify them to determine "how much" is involved. A link is provided below so you can gather further information.