An object's displacement is given by (vec{r}(t)=left(A t+B t^{3} ight) hat{t}+) (left(C-D t^{2} ight) hat{jmath}). (a) Write the expression for (vec{v}(t)) for this motion and

An object's displacement is given by \(\vec{r}(t)=\left(A t+B t^{3}\right) \hat{t}+\) \(\left(C-D t^{2}\right) \hat{\jmath}\). (a) Write the expression for \(\vec{v}(t)\) for this motion and the expression for \(\vec{a}(t)\). (b) Using the values \(A=2.0 \mathrm{~m} / \mathrm{s}, \quad B=0.10 \mathrm{~m} / \mathrm{s}^{3}, C=5.0 \mathrm{~m}\), and \(D=\) \(0.20 \mathrm{~m} / \mathrm{s}^{2}\), plot the object's position on a graph that has \(x\) as the horizontal axis and \(y\) as the vertical axis for instants \(t=0,1.0 \mathrm{~s}, 2.0 \mathrm{~s}\), and \(3.0 \mathrm{~s}\). At these positions, draw the velocity and acceleration vectors.