[MATH]a(t) = kt^2[/MATH]
[math]v(t) = \dfrac{kt^3}{3} + C[/math]
[math]v(0) = 324 \implies v(t) = \dfrac{kt^3}{3} + 324[/math]
[MATH]v(t_f) = 0 \implies \dfrac{kt_f^3}{3} = -324[/MATH] (1)
[MATH]x(t) = \dfrac{kt^4}{12} + 324t + C[/MATH]
[MATH]x(0) = 0 \implies C=0[/MATH]
[math]x(t_f) = \dfrac{kt_f^4}{12} + 324t_f = 1039.5[/math] (2)
two equations & two unknowns