Solving Flux Graphs - Need Help!

[fredrogers3]

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.

 

[rude man]

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.