A particle moves along a straight line with velocity (in m/s) for seconds

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

Problem

A particle moves along a straight line with velocity

v(t)

(in m/s) for

0\le t\le 6

seconds. It is known that

\displaystyle \int_{0}^{6} v(t)\,dt =0

while

\displaystyle \int_{0}^{6} |v(t)|\,dt =12

. Which statement best describes the particle’s motion on this interval? (a) The particle ends

12

\text{ meters} from its starting position, and it travels a total distance of

12

\text{ meters}. (b) The particle returns to its starting position, and it travels a total distance of

0

\text{ meters}. (c) The particle returns to its starting position, and it travels a total distance of

12

\text{ meters}. (d) The particle ends

0

\text{ meters} from its starting position, and it travels a total distance of

6

\text{ meters}.