The velocity of a particle is defined piecewise by v(t)= cases 3-t, & 0 t<2, [6pt] t^…

MATHEMATICS · Single correct · A Level · Mathematics · Kinematics · Kinematics

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}

t=3\text{ s}

(d) Two times, at

t=1\text{ s}

and

t=3\text{ s}