A 2-lb particle moves in the vertical \(y\) - \(z\) plane ( \(z\) up, \(y\) horizontal) under the action of its weight and a force \(\mathbf{F}\) which varies with time. The linear momentum of the particle in pound-seconds is given by the expression \(\mathbf{G}=\frac{3}{2}\left(t^{2}+3\right) \mathbf{j}-\frac{2}{3}\left(t^{3}-4\right) \mathbf{k}\), where \(t\) is the time in seconds. Determine \(\mathbf{F}\) and its magnitude for the instant when \(t=2 \mathrm{sec}\).

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Z F Up -2k lb y