Which of the following displacement time (x-t) graphs can possibly represent the one-dimensional motion of a particle?

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Solution

The correct option is D

If we draw a dotted line perpendicular to the time axis as shown below, we see that the line cuts the graph at two points A and B which means that the particle has two different positions $x_{1}$ and $x_{2}$ at the same time. This is not possible. Similarly, graphs (b) and (c) are also not possible. But graph (d) is possible.
Hence, the correct choice is (d).

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