Mathematics

Problem

Let

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

(meters) represent the position of a particle for

0\le t\le4

, where

t

is measured in seconds. The velocity of the particle is

0\text{ m/s}

t=1\text{ s}

and

t=3\text{ s}

. Which of the following statements about the motion of the particle is true? a) The particle is at a local maximum position at

t=3\text{ s}

because its acceleration is negative at that instant. b) The particle is at a local maximum position at

t=1\text{ s}

because its acceleration is negative at that instant. c) The particle is at a local minimum position at

t=2\text{ s}

because its acceleration is zero there. d) The particle is at a local minimum position at

t=1\text{ s}

because its velocity changes from negative to positive there.