How can you determine if an objects accelerating by looking at a speed vs. time graph

First, remember that 'acceleration' is any change in the object's speed or direction. So the object is accelerating if it's speeding up, or slowing down, or moving in a curve.

If it's speeding up or slowing down, then the graph of its speed vs. time is anything different from a horizontal line.

If it's moving in a curve but maintaining a constant speed, then the speed vs. time graph doesn't reveal it, although the object is technically still accelerating.