Question: 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

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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