Final answer:
The statement that the position vs time graph of an object that is speeding up is a straight line is false. A straight line on such a graph indicates constant velocity, not acceleration. The correct graph for an object that is speeding up is a curve, indicative of increasing speed over time.
Step-by-step explanation:
When considering the statement regarding the position vs time graph of an object that is speeding up, the correct answer is false. A straight line on a position vs time graph represents constant velocity, not acceleration. If an object is speeding up, the slope of the position vs time graph would be increasing, which means the graph would be curved, typically taking the shape of a parabola if the acceleration is constant. The steeper the curve, the greater the acceleration of the object.
A common mistake is to confuse the straight-line motion with constant acceleration. However, remember that straight-line graphs represent uniform motion, which means the velocity is constant and there is no acceleration. For a graph representing speeding up, acceleration is present, which translates into a changing slope on the graph.