When can an automobile with a velocity toward the north have an acceleration toward the south?

Easy...if it is going north and it is slowing down.

Because it is slowing down, you could say it has a negative northerly acceleration...which is the same thing as a positive southerly acceleration.

I think the answer is when the car is traveling northward (that's a velocity toward the north) slows down.   Slowing down is an acceleration, but it's a negative one.  So if the car is traveling north the direction of the acceleration will be south.  

Two things to remember: 1)  acceleration is a change in velocity.  2) Velocity is not technically the same thing as speed.  Velocity has two components, and speed is only one of those components.  The other component is direction.  So if you say "i'm going 20 mph", you're telling us your speed.  If you say "i'm going west at 20 mph", now you're talking about your velocity.  And if you say "I'm was moving north at 20 mph, but slowed to 15 mph" thats an acceleration, a negative one (deceleration) whose direction is south.

Here are some examples.

Velocity['s direction] is simply the direction it is moving, at whatever speed.  50km/h, 5m/s, 80mi/h, 70m/s, etc.

Acceleration doesn't have to be an increase in speed; it is used for changing velocity even if it is slowing down.  In this case it is moving one way, and the acceleration is in the other direction.  The acceleration can also be to the side.  This makes it curve to that side, often as a parabola (like in the case of gravity, or wind pushing a moving ball to the side), or as a circle which doesn't even change speed (necessarily) (like orbits), but it is still accelerating because inertia is being broken.

If the acceleration were north, in this example, it would be speeding up.  If the acceleration were south, it would slow down, and cross speed 0 and accelerate south.