If the plotted points on a speed-time graph do not form a straight line, what do you know about the object's acceleration?

Remember, that while sped is constant, acceleration is not. Acceleration is when velicity changes. So the graph which shows the slop of a velocity vs time describes acceleration.
If we have the straight line on the graph it means that the slope is always the same whereas the non-linear graphs has a variable slope that changes depending on your point in the graph.
To conclude - if your graph is not a straight line it has variable acc at many points.

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