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Steven writes:  
"... At slow speeds, assuming v = ma works OK, but it tends to   
break down when we are going really fast. ..."  
 
Give one to the real world.  In the software world it's like the   
Corvair, possibly unsafe at any speed.  However, if correct,   
it is safe at any speed.  That first "if", however, you have   
to get over.  The issue comes down to how quickly can you   
prove it correct and at what cost.  We know the shortest time   
is zero as is the least cost.  So we know where we are and   
where we want to get (at least closer) to.  We will   
determine the speed at which we get there.  
 
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