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The velocity \(v\), in \(ms^{-1}\), of a particle moving in a straight line is given by \(v=e^{3t-2}\), where \(t\) is the time in seconds.

1. Find the acceleration of the particle at time \(t = 1\).
2. For what value of \(t\) does the particle have a velocity of \(22.3ms^{-1}\)?
3. Find the distance travelled during the first second.