What is the relationship between area on a velocity / time graph?

[PotentialE]

I know that when viewing a graph in which velocity is on the y-axis and time is on the axis, the acceleration is the slope of the line. When viewing a graph in which a force is on the y-axis and a time is on the x-axis, (particularly one in which the graphed line makes a triangle) the area is the momentum. Why is it that you use the area formula for momentum and slope formula for acceleration? what is the significance of the area in a v / t graph and the slope in a F / t graph?

I have found that applying the area formula to a V / t graph gets you an answer in meters, because (1/2)*(m/s)*(s/1) = (m/2)

but I cannot seem to find a scenario in which the area correlates to any part of the problem.

In an F/t graph, the units after doing the slope formula would be kgm/s, just like momentum, accept the area is the momentum- not the slope.

Any insight?

 

[jetwaterluffy]

I found that applying the area formula to a V / t graph gets you an answer in meters, because (1/2)*(m/s)*(s/1) = (m/2)

but I cannot seem to find a scenario in which the area correlates to any part of the problem.

That would be the total displacement from the start point after time t.

 

[PotentialE]

Thanks for your answer, that is indeed what I was considering because the units cancelled. the only thing that left a doubt in my mind was this more complex graph that I have in front of me that didn't match up with it, puzzling my physics teacher and myself. But I figured it out, thank you very much!