Final answer:
An object is speeding up if its velocity and acceleration are in the same direction and slowing down if they are in opposite directions. The state of motion depends on if the velocity is increasing in the positive direction (positive acceleration) or if the velocity is positive but decreasing (negative acceleration).
Step-by-step explanation:
An object is speeding up when the direction of its velocity and acceleration are the same. If an object has a positive velocity and positive acceleration, or if it has a negative velocity and negative acceleration, it is speeding up. Conversely, an object is slowing down when the direction of its velocity and acceleration are opposite; that is, if the object has a positive velocity and negative acceleration or a negative velocity and positive acceleration.
Determining whether an object is speeding up or slowing down can be done by analyzing velocity and acceleration. As per the provided figures, an object that has a changing velocity over time demonstrates either positive or negative acceleration, corresponding to speeding up or slowing down respectively.