A particle moves on a straight line with acceleration (a(t)=alpha t+beta), with (alpha=18 mathrm{~m} / mathrm{s}^{3}) and
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A particle moves on a straight line with acceleration \(a(t)=\alpha t+\beta\), with \(\alpha=18 \mathrm{~m} / \mathrm{s}^{3}\) and \(\beta=-8 \mathrm{~m} / \mathrm{s}^{2}\). Calculate its velocity at time \(t_{1}=3 \mathrm{~s}\) knowing that the velocity at the initial time is \(v_{0}=2 \mathrm{~m} / \mathrm{s}\). Determine the space traveled between the initial time and \(t_{1}\).
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