EK Physics 1001 #82 graphs of linear motion

[ssdfrb]

im having problems figuring out this question.

82. if the graph above is a velocity vs time graph, between 6s and 8s the motion represented has:

a. positive acceleration and is backwards
b. positive acceleration and is forwards (CORRECT ANSWER)
c. negative acceleration and is backwards
d. negative acceleration and is forwards


i picked d. thinking that as the slope of the graph reaches 8 it starts to get closer and closer to 0 meaning that acceleration is constantly decreasing but still moving forward because its happening in q1.

i think im right in thinking that the direction is forwards b/c the direction of motion is occurring in q1, which is positive displacement, but why is it positive acceleration?

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[Arctangent]

As for the forward direction, I'd say that your explanation that you are in quadrant 1 definitely suffices, and confirms the direction is forward.

As far as the acceleration being positive, in a velocity versus time graph, the slope (defined as change in velocity over time in such a graph) is acceleration. The key here is that I think you did interpret that the slope is positive between 6s and 8s, though it is approaching 0, but the question is asking "is the slope negative or positive?" (acceleration), rather than "is the slope increasing or decreasing in value?" (rate of change of acceleration). I assume that the second question was answered, which would yield D.

If the graph were instead displacement versus time, the fact that the slope was decreasing to 0 would indicate a negative acceleration.

 

[Lunasly]

Exactly what arctangent. It's asking whether the slope is positive or negative rather than is it increasing or decreasing. I might be wrong here, but I believe the reason the movement is int he forward direction is because velocity is positive. Remember, velocity is a vector and we define velocity as being a positive value in the forward direction (in this case, anyway).

 

[ssdfrb]

oooh. okay. yeah im starting to see it.

im supposed to look at the slope rather than the change in slope of a v vs t graph to det'm if acc. is positive or negative.

thanks for both of the responses!