5 The curve \(C\) has parametric equations $$\mathrm { x } = \frac { 1 } { 2 } \mathrm { t } ^ { 2 } - \ln \mathrm { t } , \quad \mathrm { y } = 2 \mathrm { t } + 1 , \quad \text { for } \frac { 1 } { 2 } \leqslant t \leqslant 2$$

1. Find the exact length of \(C\).
2. Find \(\frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } }\) in terms of \(t\), simplifying your answer.