4 A particle $P$ moves on a straight line, starting from rest at a point $O$ of the line. The time after $P$ starts to move is $t \mathrm {~s}$, and the particle moves along the line with constant acceleration $\frac { 1 } { 4 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until it passes through a point $A$ at time $t = 8$. After passing through $A$ the velocity of $P$ is $\frac { 1 } { 2 } t ^ { \frac { 2 } { 3 } } \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Find the acceleration of $P$ immediately after it passes through $A$. Hence show that the acceleration of $P$ decreases by $\frac { 1 } { 12 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$ as it passes through $A$.\\
(ii) Find the distance moved by $P$ from $t = 0$ to $t = 27$.

\hfill \mbox{\textit{CAIE M1 2014 Q4}}