Algorithm to find the train's location and velocity?

[Eleanor]

I'm a silent viewer of this forum, and I came across a question I don't seem to manage...:
A train is traveling along the Z axis (infinite on both sides). You have no information as of the train's direction or speed. At each time unit the train lends on a number. At each time unit you can look at a number and find whether the train lands on it.
What can be the algorithm to find the train's location and velocity?

 

[HallsofIvy]

"A number"? Unless the numbers are somehow related to position you can't. If you are talking about a "number line" in which the numbers are in order, then the postion is given by the number and the speed the difference between two numbers "landed on" in consecutive time units, divided by the length of one time unit.

 

[Gokul43201]

Eleanor, I'm not sure any of us follow what's happening here with these numbers. Would you like to try explaining once more, perhaps more descriptively ?

 

[Eleanor]

I'll try and make myself clearer

Sorry...
By numbers I meant integers, or the Z group. Imagine that the train rail is the axis of integers, running to infinite on both sides.
You have no information as to were the train is, what is its velocity or direction.
You have a function that checks whether the train currently passes through a specific integer. The function returns yes or no only.
The only information you have is that the train must be on an integer at any such check, meaning the train can't be between two integers at the time of the check.
Hope I've managed to explain myself...
Naturally I'm familiar with the formula for velocity, but the problem here (my problem...) is to find the train. And then find it again.

 

[HallsofIvy]

You seem to be saying that there exist a function, f(x,t), that, given a time t and postion x, returns "true" if the train is at position x at time t and no if it doesn't. What one would, theoretically do, is use the "implicit function" theorem to determine x as a function of t. How you would do that depends upon the function x.

Knowing that the train MUST be at an integer at some times t doesn't really help at all.