A particle starts at the origin at

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A particle starts at the origin at t=0t=0. Its velocity (in m/s) is v(t)={2t,0≤t≤3,−3t+9,3<t≤6.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+33+\sqrt{3} (b) 6 (c) 3+63+\sqrt{6} (d) 3

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