A particle moves along a straight line so that its velocity v (in m/s) at time t seconds is given by
$v(t)=\begin{cases}
6t-9, & 0\le t\le 2,
t^{2}-4t+3, & 2< t\le 6.
\end{cases}$
The particle’s position is s(0)=5 meters.
(a) Determine the particle’s position s(6).
(b) Calculate the particle’s average velocity on the interval 0≤t≤6 and state the units.
(c) Show that there exists a time c in (0,6) at which the instantaneous velocity equals the average velocity found in part (b). Find one such value of c.
(d) Interpret the result of part (c) in terms of the motion of the particle.