an automobile is traveling north. can it have a velocity toward the north and at the same time have an acceleration toward the south? under what circumstances?

Answer 1

It is possible.

When an object is under free-fall, the direction of travel and the acceleration are both downwards.

When an object is thrown upwards, once it is in the air and ignoring air resistance, the only force acting on it is gravity. Even though it is moving upwards, the acceleration is still downwards (opposite to the direction of motion), this is why the object decellerates and eventually stops and change directions to downwards.

Answer 2

Oh, by the way, you would have been better off putting "school subject" as physics so the appropriate teacher will catch it faster.