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