A graph with horizontal axis time (seconds) and vertical axis position (meters). An orange line runs straight upward from 0 second zero meters. A concave blue line runs upward from the same point. Maia says that both lines on this position vs time graph show acceleration. Is she correct? Why or why not?

Let's start by using the definition of acceleration. Acceleration is defined as the change in velocity over the change in time. In equation, that would be Δvelocity/Δtime. Based on the axes of the given graph, it shows the trend of position over time. So, the slope of the line and the curve shows the change of position over change of time, Δdistance/Δtime. In physics, this is the definition of speed or velocity. So, Maia is incorrect. Both curves show the speed or velocity of the object, and not acceleration.  If the graph used a y-axis of velocity instead of position, then only at that instance, would be Maia be correct.

The difference between the two is, the straight line shows constant velocity while the curve line shows changing velocity.

Explanation: