Answer to Question #233708 in Calculus for johnnie

Question #233708

Assume that a particle is at the origin when the time t is at the origin

Determine the position vector of the velocity of the particle at time t given the velocity as

V(t)=e^-ti+5e^-2tj


1
Expert's answer
2021-09-07T00:51:43-0400
r(t)=V(t)dt=(eti+5e2tj)dtr(t)=\int V(t)dt=\int (e^{-t}i+5e^{-2t}j)dt

=eti52e2tj+r0=-e^{-t}i-\dfrac{5}{2}e^{-2t}j+r_0

r(0)=i52j+r0=0r(0)=-i-\dfrac{5}{2}j+r_0=\pmb{0}

r(0)=i+52j+r0r(0)=i+\dfrac{5}{2}j+r_0

r(t)=(1et)i+52(1e2t)jr(t)=(1-e^{-t})i+\dfrac{5}{2}(1-e^{-2t})j




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