A common homework problem in many introductory physics courses is similar to the following. "A car drives at constant speed over a hill on a road in the shape of a vertical circular arc. What is the maximum speed the car can have and not lose contact with the road at the crest of the hill?" Unfortunately this problem is flawed, because if the speed of the car is such that it would lose contact at the crest, then it will lose contact well before that point! In fact, the car would lose traction (i.e., the tires will begin to slip) even earlier, which can lead to a dangerous loss of steering control. The situation is worse still for an unpowered (free rolling) car, because it would travel faster at lower than higher elevations and so it would lose contact with the steeper convex road surface at a yet lower height. The present article analyzes this situation for a generalized object (not necessarily a car) of mass "m" under the following assumptions. The object is traveling either "up" a hill (everywhere inclined at less than the vertical) or on a (at least instantaneously) "level" portion of the road, so that the angle is constrained to the range 0° [less than or equal to] [theta] < 90°. For simplicity, it is assumed that there is no rolling friction or air drag. Three cases will be treated in this article: first, a rigid object that slides frictionlessly like a hockey puck on ice or on an air track; second, an unpowered object that rolls without slipping such as a ball; and third, a car that is driven by pressing on the accelerator pedal (but not so hard that the tires slip at their points of contact with the road).