6 An ice hockey puck, of mass 0.2 kg , is moving in a straight line on a horizontal ice rink under the action of a single force which acts in the direction of motion. At time \(t\) seconds, the force has magnitude ( \(2 t + 3\) ) newtons.
The force acts on the puck from \(t = 0\) to \(t = T\)
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1. Show that the magnitude of the impulse of the force is \(a T ^ { 2 } + b T\), where \(a\) and \(b\) are integers to be found.
   [0pt] [3 marks]
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2. While the force acts on the puck, its speed increases from \(1 \mathrm {~ms} ^ { - 1 }\) to \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Use your answer from part (a) to find \(T\), giving your answer to three significant figures.
   Fully justify your answer.