A particle moves along a straight line with velocity (in meters per second) for

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 meters per second) for

0\le t\le 10

. A calculator gives the following numerical results:

\displaystyle \int_0^{10} v(t)\,dt = -8\quad\text{and}\quad\int_0^{10} |v(t)|\,dt = 30.

Which statement best interprets these results? (a) The particle ends

8

\,m to the right of its starting position and travels a total of

30

\,m. (b) The particle ends

8

\,m to the left of its starting position and travels a total of

30

\,m. (c) The particle ends

22

\,m to the right of its starting position. (d) The particle’s final position cannot be determined because the given data lose direction information.