Confusion on mechanics problem involving cart, blocks, and pulley

[niko_niko]

What I see here is a formula for (b) that evaluates to $a$ which you have agreed is the acceleration of $m_1$. However, (b) was supposed to be about the acceleration of $m_2$.

I suspect that it is a correct answer for (d). Though I have not verified the formula.

What I also see here is a formula for (d) that evaluates to $a-A$ which you have agreed is the acceleration of $m_2$. However, (d) was supposed to be about the acceleration of $m_1$.

I suspect that this is a correct answer for (b). Though I have not verified the formula.

That is exactly the crux of my issue. I was able to obtain the same equations in my solution but I was utterly confused why the author seemingly did a switcheroo.

 

[jbriggs444]

That is exactly the crux of my issue. I was able to obtain the same equations in my solution but I was utterly confused why the author seemingly did a switcheroo.

So your concern all along was not with the consistency of the accelerations. Or the correctness of the solutions. It was with labelling.

 

[haruspex]

What I see here is a formula for (b) that evaluates to $a$ which you have agreed is the acceleration of $m_1$. However, (b) was supposed to be about the acceleration of $m_2$.

I suspect that it is a correct answer for (d). Though I have not verified the formula.

What I also see here is a formula for (d) that evaluates to $a-A$ which you have agreed is the acceleration of $m_2$. However, (d) was supposed to be about the acceleration of $m_1$.

I suspect that this is a correct answer for (b). Though I have not verified the formula.

Did you see post #27?
I have verified the formula for $a$.