How can an object (say, car) accelerate from some velocity to another if there is an infinite number of velocities it has to attain first?

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E.g. how can the car accelerate from rest to 5m/s if it first has to be going at 10^(-100) m/s which in turn requires it to have gone through 10^(-1000) m/s, etc.? That is, if a car is going at a speed of 5m/s, doesn’t that mean the magnitude of its speed has gone through all numbers in the interval [0,5], meaning it’s gone through all the numbers in [0,10^(-100000) ], etc.? How can it do that in a finite amount of time?

In: Mathematics

11 Answers

Anonymous 0 Comments

Step 1) Stand up

Step 2) Take step

You just moved maybe a foot, but to do that you had to cover a near infinite amount of space.

Just because there is an infinite amount something doesn’t mean you can’t go thru them. So yes, the car’s velocity went from 0 to say 5m/s and thus had to cover every possible velocity in-between in only a few seconds.

To quote YouTuber John Green (in his book A Fault in Our Stars):

> There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities

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