Q: How can an object have zero velocity and still be speeding up/slowing down?
If an object has zero velocity, and thus is not moving, how can it be speeding up or slowing down?
A: Velocity here is Instantaneous Velocity (Velocity at a time instant) and motion is a process for a certain time interval, so zero velocity doesn’t equal to Not Moving (Static)!
Think about the example of a round trip Free Fall motion: the v-t graph is a straight line with a negative slope (acceleration: -g). At the turning point (max height), the instantaneous velocity is zero, but the acceleration is always -g (non-zero!).