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Q: What is the difference between the distance vs displacement?

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Distance is a scalar and Displacement is a vector - a distance in a direction.

The dependent variable.

acceleration/decceleration it is the second derivative of a displacement vs time function

"Distance is a scalar measure of meters, and displacement is a vector measure of meters. Vectors have a direction and scalars do not. Distance is meters moved, displacement is meters moved in a specific direction." While displacement is a directed distance, that is not the key difference between the two terms. Displacement is the difference between the final position and the initial position, while distance is the length of the path connecting the two. The magnitude of displacement is the shortest distance between the final and initial positions. Example: If you walked from the southern end of your room to the northern end a total of 4 meters along a straight line, your displacement would have been +4 meters (assuming you define "north" as the positive direction). The distance you would have traveled happens to be numerically the same (4 meters). In contrast, had you walked from the southern end to the northern end not along a straight line, but along a zig-zag path, your displacement still would have been +4 meters, but the distance you traveled would have been more than 4 meters. Moreover, if after walking from the southern end to the northern end along that straight line, you then turned around and returned to the southern end via that same straight line, the distance you would have traveled would have been twice as much (8 meters), but your total displacement would have been zero.

Displacement over time, or how far an object has moved in a given time, is the definition of speed. The difference between speed and velocity is that velocity has direction.

No

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distance X time = force/moment

It is true that velocity is the slope of a displacement vs time graph.

Displacement is the area under the graph.

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The gradient of that line will be the speed of the object, because the gradient is the difference in y over the difference in x, while the speed is the difference in distance over the difference in time.

The difference is the amount of lines of resolution. From a visual standpoint, they both look great, but if you have a TV less than 40" you won't be able to tell the difference at standard viewing distance.