Solving Flux Graphs - Need Help!

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The discussion revolves around difficulties in drawing flux graphs for a homework problem. The user has attempted to illustrate the flux changes but is uncertain about the accuracy of their graphs, particularly the transition from point a to b. Another participant suggests that the rate of flux should be represented as the slope of the flux graph, advising to graph this slope onto the second figure. The conversation emphasizes the need for clarity in representing the relationship between flux and its rate of change. Accurate modeling of these graphs is crucial for solving the problem effectively.
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Homework Statement


The second picture contains the problem statement.
I am having a bit of trouble drawing the graphs asked for.

Homework Equations


See below


The Attempt at a Solution


I have drawn what I think is correct. In the first graph, I show the flux of the cart must increase from a to a/2 and go down to zero at point b. I have then used the same idea from b to a, but I am unsure if this is correct. I have modeled the rate of change in the second graph linearly, but I would like to know if it should be a trigonometric model.

Any help would be appreciated.
 

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Your rate drawing is incorrect.

The rate of flux is just the slope of the flux. So graph the slope of the top figure onto the bottom figure.
 

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