How can you tell when an object changes direction on a displacement vs. time graph

You can see it looking at the slope of the curve.

Explanation:

The slope of the curve its displacement / time, so its the celerity of the object. Now, when the object change direction of its movement, its must change the direction on which its moving, by definition. So, if the object is first getting away from its starting position, you will see its displacement grow, and the slope will be positive (or negative, it depends of the direction you put an positive displacement) Now, when its change position, the displacement will start to shrink, and the slope of the curve will be negative (or positive). To find out the exact moment in which the object changes direction, you can just look at when the slope its equal to zero. If the slope goes from positive to negative, or viceversa, it must pass by zero, the exact momento the object change direction.

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