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There is no such thing as a "slope under the curve", so I assume that you mean "slope of the curve".

If the curve is d vs. t, where d is displacement and t is time, then the slope at any given point will yield (reveal) the velocity, since velocity is defined as the rate of change of distance with respect to time. Mathematically speaking, velocity is the first derivative of position with respect to time. The second derivative - change in velocity with respect to time - is acceleration.

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Q: What does the slope under the curve of a displacement versus time reveal?
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