You have the right idea, you're just not taking the derivative correctly.
[tex]x = At^2 + Bt + C[/tex]
[tex]v = 2At^1 + Bt^0 + 0[/tex] You always decrease the power of the variable by one--but if there is no variable, then the derivate is zero---in other words: if there is no variable, it is constant, and thus the slope/change is zero.
Then the 'B' term becomes just B, and the C term drops out (is zero). ====>
[tex]v = 2At + B[/tex]
then you repeat to find the acceleration, and plug in to find the values.
Does that make sense? Make sure you review your derivatives :)
What does the acceleration equal?