(Solved): A particle moves horizontally. The distance, in cm, that the particle is to the right of the origin ...

A particle moves horizontally. The distance, in $\mathrm{cm}$, that the particle is to the right of the origin after $t$ seconds is given by $s(t)$. The graph of its velocity $v(t)=s^{?}(t)$, in $\mathrm{cm}$ per sec is shown. A positive velocity represents movement to the right. A negative velocity represents movement to the left. (a) Use the table to report and interpret $\mathrm{s}(0)$. (b) Complete the remaining entries in the table. (c) Find and interpret ${?}_0^{12}v(t)dt$. \begin{tabular}{|c|c|} \hline Time, t & Position $\mathbf{s}(\mathbf{t}),\mathbf{cm}$ \\ \hline 0 & 70 \\ \hline 2 & \\ \hline 4 & \\ \hline 6 & \\ \hline 8 & \\ \hline 10 & \\ \hline 12 & \\ \hline \end{tabular}