A particle moves along a line with velocity meters per second for seconds

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

Problem

A particle moves along a line with velocity v(t)=cos⁡t−12v(t)=\cos t-\dfrac12 meters per second for 0≤t≤2π0\le t\le2\pi seconds. Which ordered pair gives the net displacement and the total distance, in meters, traveled on this interval? (a) (−π,  3+2π3)\bigl(-\pi,\;\sqrt{3}+\dfrac{2\pi}{3}\bigr) (b) (π,  23+π3)\bigl(\pi,\;2\sqrt{3}+\dfrac{\pi}{3}\bigr) (c) (−π,  23+π3)\bigl(-\pi,\;2\sqrt{3}+\dfrac{\pi}{3}\bigr) (d) (−π,  π)\bigl(-\pi,\;\pi\bigr)

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