How can you determine if an object is accelerating by looking at a distance vs time graph?

You can't be sure.  "Acceleration" is any change in the speed
or direction of the object's motion.  You can spot a change of
speed on a graph, but it won't show you changes of direction.

If an object's speed is changing, then the graph of its distance
vs time will be curved, instead of a straight line.

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