A particle moves along a line. Its position, in meters, is modeled by s(u)=2u3−3u where u is a parameter related to time by t=u2 seconds. The interval 1≤t≤9 corresponds to 1≤u≤3.
(a) Express the particle’s position as an explicit function of time t for 1≤t≤9.
(b) Derive an expression for the velocity v(t) in terms of t on this interval.
(c) Compute the particle’s average velocity for 1≤t≤9 seconds and state the units.
(d) Determine whether there exists a time c in (1,9) at which the instantaneous velocity equals the average velocity found in part (c). Provide justification for your conclusion.