Final answer:
The statement about the position vs time graph being a straight line for an accelerating object is false, as the graph would show a curve. For Francis Cabot Lowell, the statement is true; he built the first integrated textile mill in New England.
Step-by-step explanation:
The statement that the position vs time graph of an object that is speeding up is a straight line is false. If an object is accelerating (speeding up), the position vs time graph will actually be a curve that gets steeper over time. This curvature represents increasing velocity. If the position vs time graph were a straight line, it would indicate that the object is moving at a constant speed, not accelerating.
In the context of Francis Cabot Lowell, the statement that he built the first integrated textile mill in New England is true. Lowell's establishment of the mill in Waltham, Massachusetts around 1814, marked the beginning of the factory system in the American textile industry and played a significant role in the industrial revolution in the United States.