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%  Distances and Net Change                                        %
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\problemgrouptitle{Distances and Net Change}

\item A particle oscillates in a straight line with velocity $v(t)=\sin\left(\pi t\right)$ centimetres per second. Compute the particle's displacement over the following time intervals.
\begin{enumerate}
\item $t=0$ to $t=1$ seconds.
\item $t=1$ to $t=2$ seconds.
\item $t=0$ to $t=2$ seconds. 
\end{enumerate}
\answer{ 
\begin{enumerate}
\item $\displaystyle\int_0^1v(t)\d{t}=\frac{2}{\pi}$ cm
\item $\displaystyle\int_1^2v(t)\d{t}=-\frac{2}{\pi}$ cm
\item $0$ cm (The particle is back where it started after 2 seconds.)
\end{enumerate}
}

% The following flow rate was estimated from a graph taken for the South
% Saskatchewan River at Saskatoon Saskatchewan in May 2014.
\item The flow rate at a particular location for a large river over the month of May was approximately $f(t)=-\frac{1}{3}(t-15)^2+100$ in gigalitres per day.  Here the time $t$ is measured in days from the beginning of the month.  How much water flowed past that location between the times $t=10$ and $t=20$ days?
\answer{$\displaystyle \frac{8750}{9}$ gigalitres}
