2 The coordinates of two points, \(A\) and \(B\), are \(( - 1,6 )\) and \(( 5,12 )\) respectively, where the units of the coordinate axes are metres. A particle \(P\) moves from \(A\) to \(B\) under the action of several forces. The force \(\mathbf { F } = 7 \mathbf { i } - 2 \mathbf { j } \mathbf { N }\) is one of the forces acting on \(P\).

1. Calculate the work done by \(\mathbf { F }\) on \(P\) as \(P\) moves from \(A\) to \(B\). At the instant when \(P\) reaches \(B\) its velocity is \(- \mathbf { i } - 5 \mathbf { j } \mathrm {~ms} ^ { - 1 }\).
2. Find the power generated by \(\mathbf { F }\) at the instant that \(P\) reaches \(B\). One end of a light elastic string was attached to the origin of the coordinate system and the other to \(P\) when \(P\) was at \(A\), before it moved to \(B\). The natural length of the string is 8 m and its modulus of elasticity is 24 N .
3. At the instant that \(P\) reaches \(B\), find the following.
   • The tension in the string
   • The elastic potential energy stored in the string