A particle moves along a horizontal path such that at time $t$ seconds, $t \geq 0$, its acceleration $a$ is given by $a = 2t - 1$. When $t = 6$, its displacement $s$ from a fixed point P is 18.25 m. When $t = 15$, its displacement from P is 922.75 m. Find an expression for $s$ in terms of $t$.