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Suppose that the position of a particle is given by r = AeBt i + Ae-Bt j , where A and B are constants. Find the velocity, and sketch the trajectory.

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\(\vec r=Ae^{Bt}\hat i+Ae^{-Bt}\hat j\) 

Velocity \(\vec v=\frac{d\vec r}{dt}\)

\(\vec v=\frac{d}{dt}(ae^{Bt}\hat i+Ae^{-Bt}\hat j)\) 

\(\vec v=Ae^{Bt}.B\hat i+Ae^{-Bt}(-B)\hat j\) 

\(\vec v=ABe^{Bt}\hat i-ABe^{-Bt}\hat j\)

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