Sure - unless it is a ship or air vessel
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On a three dimensional basis yes it can. Fir instance, if an object is moving directly towards or away from you the angular displacement can be zero though the distance displacement changes.
Displacement is only the distance from the starting point. As long as you return to where you started, then you can travel 1.0 x 10^999999999999 miles and still have a displacement of zero.
As, in the velocity-time graph, curves passes through zero means 'when time is zero velocity is zero'. Velocity is time derivative of displacement. So displacement is maximum or minimum when time is zero in position-time graph.
Overall, if she return to the same spot, then there is zero displacement -- they haven't moved.
They are the locations where the amplitudes of the two waves combine destructively. The positive displacement of one wave is exactly matched by the negative displacement of the other so that the overall displacement is zero.