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?

Question

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

Answer 1

This is just Zeno’s Paradox, but with velocity instead of displacement. Yes, you can perform an infinite amount of tasks, as long as you define the sum time of those tasks to be convergent. Just as Zeno’s arrow performs an infinite amount of tasks, so too does the car. It’s fine because you’ve defined those tasks to take place within a finite amount of time.