Let's take it from the other side. Instead of saying acceleration = dV/dt let's use a = F/m or acceleration equals net force applied divided by mass. Back to the ball example, without any support, the net force applied to the ball is the force of gravity, so the ball is always accelerating
until it hits the ground (and the ground provides an upward force to cancel out the force of gravity pulling downward.) If it makes it easier, think of it on the moon so you don't have to worry about air resistance. The velocity slows, goes to zero and changes direction, but the acceleration is constant so there is a time when the velocity is zero and the acceleration isn't.
In your original question, the acceleration is in the northern direction. If the initial velocity was in the southern direction, there will come a time when the object will stop going south and turn north. At that moment, the velocity is zero but it is still accelerating.