A particle moves with velocity (in meters per second) v(t)= cases 3t, & 0 t 2, 12-3t,…

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

Problem

A particle moves with velocity (in meters per second)

v(t)=\begin{cases} 3t, & 0\le t\le 2,\\ 12-3t, & 2<t\le 6,\\ -6, & 6<t\le 8. \end{cases}

What is the total distance the particle travels over the interval

0\le t\le 8

seconds? (a)

27\,\text{m}

(b)

24\,\text{m}

(c)

30\,\text{m}

(d)

18\,\text{m}