Question

A particle moves along the space curve r=e-t(cos⁡t i+sin⁡t j+k). Find the magnitude of the veloctiy at any time t.

Select one:

A 5e-1

B 5e-t

C 3e-1

D 3e-t

Answer 1

$\frac{dr}{dt}=\frac{d}{dt}\left( e^{-t}\cos t,e^{-t}\sin t,e^{-t} \right) =\left( -e^{-t}\cos t-e^{-t}\sin t,-e^{-t}\sin t+e^{-t}\cos t,-e^{-t} \right) \\\left| \frac{dr}{dt} \right|=\sqrt{\left( -e^{-t}\cos t-e^{-t}\sin t \right) ^2+\left( -e^{-t}\sin t+e^{-t}\cos t \right) ^2+\left( -e^{-t} \right) ^2}=\\=\sqrt{3}e^{-t}$