1. A particle \(P\) moves in a straight line so that its velocity \(v \mathrm {~ms} ^ { - 1 }\) at time \(t\) seconds is given, for \(t > 1\), by the formula \(v = 2 t + \frac { 8 } { t ^ { 2 } }\). Find the time when the acceleration of \(P\) is zero. (5 marks)

A key is modelled as a lamina which consists of a circle of radius 3 cm , with a circle of radius 1 cm removed from its centre, attached to a rectangle of length 8 cm and width 1 cm , with a rectangle measuring 3 cm by 1 cm fixed to its end as shown. Calculate the distance of the centre of mass of the key from the line marked \(A B\).