Mathematics

Problem

A particle moves along a straight line so that its displacement is

x(t)=t^{3}-6t^{2}+9t

(metres) for

0\le t\le 3\,\text{s}

. a. (i) Compute the average velocity of the particle for the interval

0\le t\le 3\,\text{s}

. b. (ii) Show that there exists at least one instant

t

in the open interval

(0,3)

when the instantaneous velocity equals this average velocity. Determine all such value(s) of

t