Mathematics

Problem

The velocity of a particle is defined piecewise by

v(t)=\begin{cases} 3-t, & 0\le t<2,\\[6pt] t^{2}-4t+3, & 2\le t\le 5, \end{cases}

where

t

is measured in seconds. How many times, and at which time(s), does the particle change direction on

0\le t\le 5

? a) Two times, at

t=2\text{ s}

and

t=4\text{ s}

b) Two times, at

t=2\text{ s}

and

t=3\text{ s}

c) One time, at

t=3\text{ s}

d) Two times, at

t=1\text{ s}

and

t=3\text{ s}