Let's look at the position x x= vot + 1/2 at^2 vo = original velocity
solve for vo
vo = x/t- 1/2at
Now, the VELOCITY at x Vx= vo + at
Substitute for vo to get
Vx = (x/t -1/2at) +at
Vx = x/t +1/2at
Now, for y
y =vt' + 1/2at'2 In THIS instance the 'v' is Vx which we found above, so let's substitute this into the equation
y= (x/t + 1/2at) t' + 1/2at'^2 now solve for a
y-xt'/t = 1/2a (tt' +t'2)
2 (y-xt'/t) = a t'(t+t')
a= 2(y-xt'/t) / (t' (t+t') ) Simplify
a= 2(y/t' -x/t) / (t+t')