Final answer:
An object that is speeding up can have either positive or negative acceleration, depending on the direction of its motion relative to the chosen coordinate system. Acceleration is a vector, and when it matches the direction of the object's velocity, the object will speed up.
Step-by-step explanation:
If an object is speeding up, its acceleration can be positive or negative depending on the direction of motion. Acceleration is a vector and represents the rate of change in velocity. An object speeding up implies that its acceleration is in the same direction as its velocity. For example, if a car is moving to the right (positive direction) and speeding up, it has positive acceleration. Conversely, if a car is moving to the left (negative direction) and speeding up, then its acceleration is negative because it is accelerating in the same direction as its negative velocity.
It is important to note that acceleration does not solely depend on whether the object's speed is increasing but also the direction of its velocity compared to the coordinate system being used. Thus, an object can have negative acceleration and still be speeding up if its velocity is also negative, moving it faster in the negative direction.