Vectory, velocity kinematics. HELP

Well, what have you tried?
It would be helpful to see which method you tried, because I have two in mind...

I have subbed the values 2i +5j, -2.5i +8j and 3 in the formulae r = r 0 + v t to get 2i +5j = -2.5i +8j + 3v ans then rearranged to get 1.5i-j = v. Then subbed these values into thr formulae v = u + at to get 1.5i -j = u + (i-2j)3 then got the value of u to be -1.5 + 5j. However the answer is (-3i + 4)
(I am new to this topic so apologise if I've broken maths here😅)

Ah, okay, you've gone the suvat route.
I think what you've gone wrong is using $r = r_{0} + ut$ - this formula assumes the particle is moving at constant velocity and with no acceleration. (Beware of the "v" here. This v is almost but not quite the the same v in suvat.)

But the idea is there - you just need to factor in acceleration... but wait, we already have a suvat formula for it, namely $\displaystyle s=ut+\frac{1}{2}at^{2}$. (In fact, $r = r_{0} + ut$ is just a simplified version of this. We set a=0 and s to actually calculate displacement, and we'll get that.)

Of course the problem is the s. This s is the displacement, not the position. So if you know what displacement is (as in if you really know the concept of it), you should be good to go.