Final answer:
An object having constant velocity and variable acceleration is the impossible situation. Velocity is a vector that includes both speed and direction, so if an object's velocity is constant, its acceleration, which is the rate of change of velocity, must be zero.
Step-by-step explanation:
The situation that is impossible is B) An object having constant velocity and variable acceleration. By definition, acceleration is a change in velocity, which includes changes in either speed or direction. If an object has a constant velocity, its speed and direction remain the same, meaning that acceleration must be zero. Therefore, an object cannot have a constant velocity and at the same time have a variable acceleration.
For situation A), an object can have a constant acceleration and still have a variable velocity. An example of this is an object in free fall, where gravity provides a constant acceleration, while the object's velocity increases as it falls.
In situation C), an object can have a velocity pointing north and acceleration pointing south, which typically means the object is slowing down as it moves north.
Situation D) is also possible; when an object has a zero velocity and non-zero acceleration, it may be starting its motion or just changing the direction of motion. This can happen at the very beginning of movement when an object starts to move from rest, or at the peak of motion in vertical launch where velocity is momentarily zero before descending.
Last, in situation E) having velocity and acceleration in the same direction (north) means the object is speeding up as it moves north.