- #1
doktorwho
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Homework Statement
Given the ## r(t) = ae^{kt}## , ##θ(t)=kt## find the velocity function that is dependent on ##r##.
##v(r)=?##
Homework Equations
3. The Attempt at a Solution [/B]
My attempt:
1)##r(t) = ae^{kt}##
2)##{\dot r(t)} = ake^{kt}##
From the first equation:
##\ln {\frac{r(t)}{a}}=\ln e^{kt}##
##\ln {\frac{r(t)}{a}}=kt##
##t=\frac{\ln {\frac{r(t)}{a}}}{k}##
Replacing the ##t## in the second equation i get:
##{\dot r}=akr##
Shouldn't this be the answer? In the answers it says ##{\dot r}=\sqrt2r##?
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