Mathematics

Problem

A particle starts at the origin at

t=0

. Its velocity (in m/s) is

v(t)=\begin{cases} 2t,&0\le t\le 3,\\ -3t+9,&3< t\le 6. \end{cases}

At what time, in seconds, does the particle first return to the origin? a)

3+\sqrt{3}

b) 6 c)

3+\sqrt{6}

d) 3