Let me make somethings very clear here for the sake of discussion:
Here we have to define whether or not we are talking of instantaneous velocity or simply velocity. As Raff touched the topic of Calculus (and also in almost all cases of studying the Newtonian Model of Classical Mechanics), most of the time we are dealing with instantaneous velocity, which as the name suggest, is the velocity of the object at the instant of time. In case the object starts and ends at the same point, once it has come to rest, both it's velocity and speed are zero. But just before that (and here comes deltas) at a moment of time it was not at the same place (it couldn't be as it is moving in some direction) and thus it will have velocity.

Now consider a man walking on the tread mill, does he have velocity (or speed)? Neither because there is no displacement (huh ? the odometer is lying and I am sweating for nothin'). We always need to consider instantaneous stuff. Specially in our field it is of utmost importance as we are dealing with simulation and particles.

Off topic, just for fun - Go read Zeno's Achilles and tortoise paradox (if you haven't already), which is somewhat related. You'll have fun !

On 13/02/2013 4:32 PM, Matt Lind wrote:

If you make a complete lap in 60 seconds, then your speed is 6.66 meters per second, while your velocity is 0 meters per second because you haven't been displaced from your starting position.

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