The velocity of an object is given in SI units by (vec{v}=left(a t-b t^{2} ight) hat{imath}+c hat{jmath}),

The velocity of an object is given in SI units by \(\vec{v}=\left(a t-b t^{2}\right) \hat{\imath}+c \hat{\jmath}\), with \(a=14 \mathrm{~m} / \mathrm{s}^{2}, b=10 \mathrm{~m} / \mathrm{s}^{3}\), and \(c=22 \mathrm{~m} / \mathrm{s}\).

(a) If the initial position of the object at \(t=0\) is at the origin \(\left(x_{\mathrm{i}}=y_{\mathrm{i}}=0\right)\), when, if ever, does the object return to the origin?

(b) When, if ever, is the velocity zero?

(c) When, if ever, is the acceleration zero?