1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors directed due east and due north respectively.]

A particle \(P\) moves with constant acceleration \(( - \lambda \mathbf { i } + 2 \lambda \mathbf { j } ) \mathrm { ms } ^ { - 2 }\), where \(\lambda\) is a positive constant. At time \(t = 0\), the velocity of \(P\) is \(( 5 \mathbf { i } - 8 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)

1. Find the velocity of \(P\) when \(t = 5 \mathrm {~s}\), giving your answer in terms of \(\mathbf { i } , \mathbf { j }\) and \(\lambda\). The speed of \(P\) when \(t = 5 \mathrm {~s}\) is \(13 \mathrm {~ms} ^ { - 1 }\)
2. Show that $$25 \lambda ^ { 2 } - 42 \lambda - 16 = 0$$
3. Find the direction of motion of \(P\) when \(t = 4 \mathrm {~s}\), giving your answer as a bearing to the nearest degree.