I guess now your solve block models the current limitation correctly, assuming a(n ideal) current limiting device in series with the motor.
I keep my doubts about the simulink graph.
The current limiting 'device' is just academic at the moment. I'm not much for electrons so won't even speculate on what it could be. Also, at least for this problem, I'm told kt = 1/ks. I believe this is derivable but haven't done it myself yet. Also, I believe the simulink answer is actually per this picture - I'd previously been plucking the wrong current.
yes, although that is completely arbitrary - just done to show what happens before voltage is applied. Starting at t=0s is fine.
Now your curve matches the (corrected) curve of DJF. Two independent methods arriving at the same answer. That gives confidence.
Unfortunately (for me) Mathcad 11 doesn't like the construction with the min():
That is: it refuses to limit i(t) to 10 !
But strangely the w(t) curve resembles yours...