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AP Calculus AB/Unit 8: Applications of Integration
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Particle Position from Velocity

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The velocity of a particle moving along the xx-axis is given by v(t)=3sin⁡(2t)+1v(t) = 3\sin(2t) + 1. At time t=0t=0, the position of the particle is x=2x=2. What is the position of the particle at time t=π2t = \displaystyle\frac{\pi}{2}?

A

5+π25 + \displaystyle\frac{\pi}{2}

B

6+π26 + \displaystyle\frac{\pi}{2}

C

4+π24 + \displaystyle\frac{\pi}{2}

D

3+π23 + \displaystyle\frac{\pi}{2}

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