Why is there a velocity associated with escaping from earth’s atmosphere? If an object were to fly from the surface of the planet at 1 m/s without any change in acceleration would it not eventually end up in space?
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You have to be moving fast enough that gravity never pulls you back.
As things get further away, the pull of gravity becomes weaker.
Imagine a slope that starts to level off at the top. You can roll a ball up the slope and have it roll back to you. But if you roll it fast enough, it can make it up to the “top” of the slope and never come back.
Edit. OP was accounting for constant acceleration in their perspective. That’s not something you consider when looking at escape velocity, and I completely overlooked that in my answer.
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