Ok let me try to explain this well know fact to you as best i can
An object cannot simply change from on velocity to another instantaneously. We use Einsteins Force = mass X Acceleration to work this out. So as you apply force to an object to alter its velocity there is a finite level of acceleration that can be generated bounded by the mass of the object and the force applied to it.
In this extreme case the force available is very large and the mass of the fly is very small so the acceleration achievable is very high but not infinite.
If the acceleration is finite, then the change in velocity is also finite, so therefore there is a velocity profile starting with the steady state velocity before the impact and ending with the steady state velocity after the impact.
Perfectly correct up to that point.
If you plot the velocity of the two objects both before and after the impact there will be a finite length of time where the two objects (after contact) are at zero velocity because the smaller object started at a negative velocity relative to the train and changes to a positive velocity.
This is where it breaks down - the velocity of the train has nothing to do with the velocity of the fly, and coming back to the original question, 'Does the fly stop the train', the answer is no. It's a question posed by Cambridge physics professors to get people to think, and the answer is no, Not my answer, but theirs. The RELATIVE velocity of the two objects might be said to be zero at an instant in time, but that's a very different concept. My relative velocity to this laptop is zero, but we are both zipping round the sun at an awesome pace.
The puzzle is more difficult to accept because every one knows that fly's hit trains and cars all the time and have no effect. If the question had been a house brick then the mass would be larger and the force larger, causing the surface of the train to experience much higher forces to create the change in velocity of the brick and so damage occurs.
It is not however true to assume that the force to alter the velocity of a fly is zero, it will be very small and the force experienced by the small area on skin of the train to create the acceleration will be so small that it will likely allow the trains skin to flex and return to an undamaged state, but it must exert force on the fly (or the mass of the fly, since it will change a bit in this process) and will be at zero velocity for perhaps a few nanoseconds or less, not sure, but it is inherently true and this is evident both from the know law that F=ma and also intuitively true if you consider larger objects, like birds or house bricks.
I was told this puzzle by an eminent university professor who used it to make his students think clearly about things, so its not my questions sir, and as far as I am aware this is a known fact and not an act of belief on my part.
I gave you the approximate energy levels and the force required to change the velocity of the fly - I certainly didn't assume it was zero. BUT, and it's something you are apparently not grasping, the fact that one object is accelerated from zero to the velocity of an impacting object does not mean the impacting object has to have a velocity of zero, even momentarily.
Using F=ma is fine up to a point; it tells us what happens to the fly and indeed the train, but it doesn't tell us anything about the velocity of the two objects.
You can try to look at atomic particles and consider that one fly molecule hitting one train molecule will cause the train molecule to reduce its velocity to zero, but it still doesn't work I'm afraid... You need to look at the energy levels too - the train molecule has higher energy (19x higher in your example, assuming the molecules have identical mass). Even in this example, the plotted velocity of the train molecule doesn't drop to zero on impact.
It's very much a provable fact that the train isn't stopped by the fly, no matter how you look at it!
Still, if you can prove to me otherwise, I'm happy to take the proof along to Trinity for the physics faculty to examine.