Final answer:
The statement is false; an object speeding up will have a curved position vs time graph, typically a parabola, indicating acceleration.
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. When an object is speeding up, its velocity is changing over time, which means the object is accelerating. A position vs. time graph for an object that is accelerating will not be a straight line; instead, it will be a curve, indicating that the speed is not constant. For uniform acceleration, this graph will typically be a parabola. A straight line on a position vs time graph indicates constant velocity, not acceleration. This would result in a curved graph rather than a straight line.
For example, if you plot the position of a car as a function of time and the car is accelerating, the graph would show a curved line because the car is covering more distance in less time as it accelerates.