> 3000=0*t+0.5at^2+(100/9)*t+0.5a*3t^2+100/9*16t

Your equation is a real puzzle!

Why include 0*t ? Why is 100/9 bracketed, then not bracketed?

Is it this:

[a t^2 / 2] + [100 t / 9] + [3a t^2 / 9] + [1600 t / 9] = 3000 ?

If so, that easily simplifies to:

9 a t^2 + 850 t - 13500 = 0

So both a and t easily solved for.