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A bug travels along a curved path with a velocity given by:

$$v(t)=\sin\left( \frac { \pi t }{ 2 } \right) \text{cm/s}$$

What total distance does the bug travel in the first three seconds?

$ \cfrac {3\pi }{ 2 } \text{cm} $

$ \cfrac { 2 }{ \pi } \text{cm} $

$ \cfrac { 4 }{ \pi } \text{cm} $

$ \cfrac { 6 }{ \pi } \text{cm} $