Uniformly Accelerated Motion: A Puzzling Problem?

[ilp89]

The problem statement:

A particle travels along the x-axis with uniformly accelerated motion. At times t and s its position is x and y, respectively. Show that its acceleration is a = 2(yt-xs)/ts(s-t).

The attempt at a solution:

I could be wrong, but it seems to me this problem is ill-posed. Couldn't one solution be a = 0? Couldn't another be that acceleration which gets the particle from rest at (x,t) to (y,s)?

 

[gneill]

It does seem to be ill-posed; A particle can get from one point to another (from x to y) in a given time interval using any choice of initial speed and a suitable constant acceleration. Another data point of some kind would be required to make the problem determinate.