Question

There is a parabolic position vs time graph.

Which of these is true:

The object moves

1. in a parabolic trajectory.
2. along a straight line.
3. along an arc of a circle

wouldn't 1 and 3 produce the same/similar position graph?

Answer 1

No, #1 and #3 would be different trajectories. Note that they are asking about position vs. time, not about the shape of the trajectory

Answer 2

So in which one would the graph of position vs time be a parabola?

If the object moves along a straight line, then wouldn't the position graph just be an increasing line with with positive slope?

Answer 3

If position vs time is a parabolca, the object is accelerating at a constant rate along a straight line.