If a velocity-time graph has a static trend, i.e., neither moving up or down (starting at (0,50) and (for the purposes of the graph) ending at (10,50), then what would the acceleration-time and distance-time graphs look like?

Answer 1

The acceleration graph would be a straight line coincident with the time-axis.
The distance graph would be a straight line with a distance:time slope of 50.

If the velocity graph is a horizontal line, the velocity is constant, which means that there is no acceleration.

With a constant velocity of 50 the distance travel during a time period #Delta t# would be #50*Deltat#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.