How does a particle carry the information that it is in motion from one instant to another?

Assuming that a particle is in motion, then at any given instant in time that particle must momentarily be at rest, so just how (and where) does it store the information about its velocity, that can be carried to a subsequent instant of time?How does a particle carry the information that it is in motion from one instant to another?I assume you are just getting into Calculus. Your question goes to the most basic part of what the Calculus is and how it works. The information is "stored" in "differential time."



Differential time = time interval approaches 0 as closely as we wish it to. We solve for:



Velocity = distance/differential time = dd / dt



Newton's insight:



If velocity is constant, then we just divide distance by time, but what to do if velocity is changing (acceleration)? ====%26gt; We can estimate the average velocity by taking shorter and shorter time intervals near the time or distance of interest. Now it gets interesting. The shorter the time interval the more accurate the estimate of velocity. If the time interval shrinks to 0, then we would have velocity at that instant of time. BUT, that means we would divide by 0 and mathematics does not allow division by 0. Enter: differential time. Newton thought, "What if we cheat? What does velocity approach as time interval approaches 0? We can say time interval is infinitesimally small (very very close to 0 but not quite there) then velocity approaches the true instantaneous value. Technically we can never know the instantaneous velocity (We cannot divide by 0), BUT we can get as close to it as we wish (We can divide by dt), close enough!



Your question is one of Zeno's Paradoxes



http://en.wikipedia.org/wiki/Zeno's_para鈥?/a>



The solution like Calculus lies in the concept of a Limit.



Now, I am going to really mess with your mind.



What if time and space are NOT continous?



There may be no such thing as 0 time for a physical process. Time may not be continous, but particulate. There may be quanta of time.



and



distance may also be particulate.



http://en.wikipedia.org/wiki/Planck_leng鈥?/a>



http://en.wikipedia.org/wiki/Chronon



If so, your question is moot. Objects move from planck length to Planck Length in one chronon.How does a particle carry the information that it is in motion from one instant to another?It has the teeniest of tiniest of laptop computers with a massive memory bank! :-)