Consider the parametric curve $$\mathbf{r}(t)=\left<t^{2},-t^{3}\right>.$$ Determine which of the following graphs is the correct image of this curve:

Also, compute the velocity and acceleration vectors at $t=1$, and use this information to determine the direction of motion for the curve.

The correct graph is (Select One) A B C D .
$\mathbf{v}(1) =$ .
$\mathbf{a}(1) =$ .
The direction of motion is Left-to-Right Top-to-Bottom Bottom-to-Top Right-to-Left (Select One) .

Usage: To enter a vector, for example $\langle x,y,z\rangle$, type "$<$ x, y, z $>$"