1. \hspace{0pt} [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors and position vectors are given relative to a fixed origin \(O\) ]

A particle \(P\) is moving on a smooth horizontal plane.
The particle has constant acceleration \(( 2.4 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\)
At time \(t = 0 , P\) passes through the point \(A\).
At time \(t = 5 \mathrm {~s} , P\) passes through the point \(B\).
The velocity of \(P\) as it passes through \(A\) is \(( - 16 \mathbf { i } - 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\)

1. Find the speed of \(P\) as it passes through \(B\). The position vector of \(A\) is \(( 44 \mathbf { i } - 10 \mathbf { j } ) \mathrm { m }\).
   At time \(t = T\) seconds, where \(T > 5 , P\) passes through the point \(C\).
   The position vector of \(C\) is \(( 4 \mathbf { i } + c \mathbf { j } ) \mathrm { m }\).
2. Find the value of \(T\).
3. Find the value of \(c\).