Final answer:
The statement is false because the position vs time graph of an object that is speeding up will show a curved line due to acceleration, not a straight line.
Step-by-step explanation:
The position vs time graph of an object that is speeding up is not a straight line, so the answer to this question is false. If an object is speeding up, this means it is accelerating, and its velocity is increasing over time. Consequently, the position vs time graph of such an object will show a curve, not a straight line. A straight line on a position vs time graph indicates constant velocity, not acceleration.