The velocity of an object moving along a straight line is given by the function
\[ v(t) = \begin{cases} t-2 & 0\leq t\leq 4\\ 2\cos \left (\frac {\pi t}{2}\right ) & 4<t\leq 8\\ \end{cases}. \]
[\(v\) is
measured in m/s and \(t\) in seconds.]
The velocity attains its maximum at \(t=\answer {4}\) s and \(t=\answer {8}\) s (answer from left to right).
The velocity is zero at \(t=\answer {2}\) s, \(t=\answer {5}\) s, and \(t=\answer {7}\) s (answer from left to right).
The total distance the object travels on the interval \([0,4]\) is \(\answer {4}\) m.
The total distance the object travels on the interval \([0,8]\) is \(\answer {4+\frac {16}{\pi }}\) m.
The displacement of the object on the interval \([0,8]\) is \(\answer {0}\) m.
The average velocity of the object on the interval \([0,8]\) is \(\answer {0}\) m/s.