My book states that the distance traveled by a particle thrown upward in the last second is independent of it's initial velocity because the the object travels the same distance as a freely falling body in $1^{st}$ second. But I have two concerns related to this:
Can't it be extended to the case for the distance traveled in $n^{th}$ second? My logic is that since the motion of the particle would be the same in forward as well as backward direction of time therefore distance traveled by it in $n^{th}$ second must be independent of the initial velocity.
Suppose that for the course of the motion the forces acting on it ceases to exist, then the distance traveled by the particle in $n^{th}$ second must be "$u$" meters. ( $u$ being the initial velocity). Hence,I conclude that even the case for accelerated motion must depend on initial velocity.
I am currently confused between the two (the fact that it should deped and it should not). So my question is would it depend on initial velocity or not? (If so how? Why?)