Suppose that the position of a particle is given by r = Aexp^(Bt) i + Aexp^(-Bt) j ,

Question

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

Answer 1

Given 

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

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

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

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

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