Thanks to Brian and David for helping me. Let me tell
you how the issue came about; some of you may prefer
to make my mistake deliberately.
We solved this problem in class (#5.23 in College Physics
of Sewray, 5th edition) using the energy conservation
principle and as an additional challenge I suggested we
check if we get the same results directly from F=m*a. I did
not hide the discrepancy and told students that physics
problems are often challenging, even to teachers. Let me
think about this at home, I said. Now I know how to
resolve the "paradox". Thanks again.
Ludwik Kowalski