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AP Calculus BC/Unit 8: Applications of Integration
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Particle Motion Initial Value Problem

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A particle moves along the xx-axis with acceleration a(t)=6cos⁡3ta(t) = 6\cos 3t for time t≥0t \geq 0. If the velocity of the particle at t=0t=0 is v(0)=−2v(0)=-2 and its position at t=0t=0 is x(0)=4x(0)=4, then the position of the particle at time tt is x(t)=x(t) =

A

−23cos⁡3t−2t+143-\frac{2}{3}\cos 3t - 2t + \frac{14}{3}

B

23cos⁡3t−2t+103\frac{2}{3}\cos 3t - 2t + \frac{10}{3}

C

−2cos⁡3t−2t+6-2\cos 3t - 2t + 6

D

−23cos⁡3t−2t+4-\frac{2}{3}\cos 3t - 2t + 4

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