Answer
$y=\dfrac{2}{9}x^2$; $v(\ln 3)=3i+4j$ and $a(\ln 3)=3i+8j$
Work Step by Step
We know that the velocity and acceleration is defined as: velocity is given as: $v(t)=r'(t)$ and acceleration is given as: $a(t)=v'(t)$
In the given problem, we have
$x=e^t; y=\dfrac{2}{9}e^{2t}$
Re-write as follows: $y=\dfrac{2}{9}x^2$
$v(t)=r'(t)=e^ti+\dfrac{4}{9}e^{2t}j\\ \implies v(\ln 3)=3i+4j$
Next, we have $a(t)=v'(t)=e^ti+\dfrac{8}{9}e^{2t}j\\ \implies a(\ln 3)=3i+8j$
