Final answer:
The correct option is v. a body travels with a constant velocity and a time-varying acceleration.
Step-by-step explanation:
The situation that is not possible is iv. a body travels with a constant velocity and a time-varying acceleration. This is because acceleration refers to the rate of change of velocity. If a body has constant velocity, it means there is no change in velocity, and therefore, the acceleration must be zero. If acceleration were to vary while velocity is constant, it would contradict the very definition of acceleration.
Regarding the other situations: i. A body has zero velocity and non-zero acceleration, such as a car at the top of a hill just as it starts to roll down. ii. A body travels with a northward velocity and a northward acceleration, for instance, a speedboat increasing its speed while moving north. iii. A body travels with a northward velocity and a southward acceleration, an example being a car slowing down as it continues to move north. Lastly, v. A body travels with a constant acceleration and a time-varying velocity, like an object in free fall under gravity's constant acceleration.