Figure 11.20 shows the velocities \(\vec{v}_{\mathrm{i}}\) and \(\vec{v}_{\mathrm{f}}\) of a point on the rim of an object at two instants \(t_{i}\) and \(t_{t}\) for four different motions. For each case, determine the change in velocity \(\Delta \vec{v}\) and the direction of the average acceleration at a point in time halfway between \(t_{\mathrm{i}}\) and \(t_{\mathrm{f}}\).

Data from Figure 11.20

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(a) (b) (c) (d)