Physics
posted by Elisa .
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?

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

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