M5 June 2014 (R) Q1

1. [In this question, \(\mathbf{i}\) and \(\mathbf{j}\) are perpendicular unit vectors in a horizontal plane.]

A bead \(P\) of mass 0.2 kg is threaded on a smooth straight horizontal wire. The bead is at rest at the point \(A\) with position vector \((4\mathbf{i} - \mathbf{j})\) m. A force \((0.2\mathbf{i} + 0.3\mathbf{j})\) N acts on \(P\) and moves it to the point \(B\) with position vector \((13\mathbf{i} + 5\mathbf{j})\) m.

Find the speed of \(P\) at \(B\). (5)