Well,
Let's just say that the Jaguar! (a certain ride in Knott's) could instantly go from zero speed to, let's say, 40 mph, and vice versa. We know (if you have ridden it) that the Jaguar! is not a straight line, as you can't say that it is always traveling at 40 mph due north (otherwise it would never be able to make a loop)!
Remember that, since velocity is a vector quantity, a change in direction will constitute a change in velocity.