deceleration with fixed distance over time

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Hi I'm doing a bit of mobile phone game development using a physics engine and have come across a mathematics problem thats stumped me.

basically

object A has a velocity vector of dx:0, d:300

object B has a velocity vector of dx:0, dy:300

object A leads object B by 200 points

something happens to object B and its velocity reduces to dx:0 dy:0

And here is what the problem:

I need to reduce the velocity of object A over time, so that after 0.25 seconds object A has travelled 150 points and its velocity matches that of object B.

I don't know how to calculate by how much I should reduce the velocity of object A for any point of deltaTime.

If it was straight interpolation then I can get it but because the changing velocity changes the distance and keeping it the 0.25 seconds I'm stuck!

I really hope this problem makes sense and some one can either show or just direct me to what I need to learn to figure this out

BR

Danny