Fly hits windscreen

[lurch]

My science teacher posed this question at school and I missed the next lesson and the answer has been bugging me for ten years now! It goes like this...

A car is travelling in one direction at 30 mph and a fly is travelling head-on towards it at 5mph. As the fly hits the windscreen it goes from travelling 5mph in one direction to 30mph in the other direction. This means that at some point the fly MUST have been travelling at 0mph. And because the fly was travelling at 0mph the car must also have been travelling at 0mph. Which means that the fly stopped the car!

I know that fliss don't stop cars - so what is the answer to this science riddle?

[incitatus]

The question contains a logical fallacy. If you draw the graph of fly distance vs time then it will be a hyperbolic type curve, with an assymptote at which the fly speed=0. If you draw a similar graph for the car it will not show the car doing more than slowing very slightly. The point is that although there is a point at which the first order differential for fly dx/dt (speed) is 0, this instant is a mathematical point, i.e. it is for an infinitely small time. This is basically calculus, rather than gross slope calculation. In other words the moment at which the fly is travelling at 0mph is only a notional moment, it has no duration.