5 The velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of a particle moving along a straight line is given by $$v = 3 t ^ { 2 } - 12 t + 14$$ where \(t\) is the time in seconds.

1. Find an expression for the acceleration of the particle at time \(t\).
2. Find the displacement of the particle from its position when \(t = 1\) to its position when \(t = 3\).
3. You are given that \(v\) is always positive. Explain how this tells you that the distance travelled by the particle between \(t = 1\) and \(t = 3\) has the same value as the displacement between these times.
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