I remember a question that goes down like this. Imagine two balls starting with the same initial velocity on separate paths. It looks like THIS (ignore that they aren't at the same position in the drawing - a mistake).

Which one finishes the path quicker?

I remember this way of reasoning that concludes that the 2nd ball will come quicker.

We are observing only the x-axis, since y-axis motion is irrelevant for the question posed. Both balls cover the path from 1 to 2 in the same time. However, from 2 to 3 the 2nd ball accelerates and covers that path in less time than the 1st ball. From 3 to 4 the 2nd ball is moving with a new velocity higher than the velocity of the 1st ball thus again the 2nd ball covers that path as well faster than the 1st ball. Now from 4 to 5, the 2nd ball is experiencing negative acceleration, however the velocity of the 2nd ball is again always greater than the velocity of the 1st ball and thus again the 2nd ball covers that portion in less time than the 1st ball. Now the 2nd ball has made substantial advantage over the 1st ball, and thus their separation distance is constant from 5 to 6. Now this seems reasonable to some extent but incredibly counterintuitive and I am having trouble understanding this to the fundamentals.

I remember a question that goes down like this. Imagine two balls starting with the same initial velocity on separate paths. It looks like this:

(ignore that they aren't at the same position in the drawing - a mistake).

Which one finishes the path quicker?

I remember this way of reasoning that concludes that the 2nd ball will come quicker.

We are observing only the x-axis, since y-axis motion is irrelevant for the question posed. Both balls cover the path from 1 to 2 in the same time. However, from 2 to 3 the 2nd ball accelerates and covers that path in less time than the 1st ball. From 3 to 4 the 2nd ball is moving with a new velocity higher than the velocity of the 1st ball thus again the 2nd ball covers that path as well faster than the 1st ball. Now from 4 to 5, the 2nd ball is experiencing negative acceleration, however the velocity of the 2nd ball is again always greater than the velocity of the 1st ball and thus again the 2nd ball covers that portion in less time than the 1st ball. Now the 2nd ball has made substantial advantage over the 1st ball, and thus their separation distance is constant from 5 to 6. Now this seems reasonable to some extent but incredibly counterintuitive and I am having trouble understanding this to the fundamentals.