M5 June 2007 Q1

1. A bead of mass 0.5 kg is threaded on a smooth straight wire. The only forces acting on the bead are a constant force \((4\mathbf{i} + 7\mathbf{j} + 2\mathbf{k})\) N and the normal reaction of the wire. The bead starts from rest at the point \(A\) with position vector \((\mathbf{i} + 2\mathbf{j} + 3\mathbf{k})\) m and moves to the point \(B\) with position vector \((4\mathbf{i} + 3\mathbf{j} - 2\mathbf{k})\) m.

Find the speed of the bead when it reaches \(B\).