Answer
$y=\dfrac{2}{9}x^2$; $v(\ln 3)=3i+4j$ and $a(\ln 3)=3i+8j$
Work Step by Step
Since, we have $x=e^t; y=\dfrac{2}{9}e^{2t}$
This can be written as:
$y=\dfrac{2}{9}x^2$
Now, velocity $v(t)=r'(t)=e^ti+\dfrac{4}{9}e^{2t}j$
and $v(\ln 3)=3i+4j$
As we know acceleration $a(t)=v'(t)=e^ti+\dfrac{8}{9}e^{2t}j$
and $a(\ln 3)=3i+8j$
Hence, we have $y=\dfrac{2}{9}x^2$; $v(\ln 3)=3i+4j$ and $a(\ln 3)=3i+8j$
