The figure given below shows the displacement and time, $(x-t)$ graph of a particle moving along a straight li

Question

The figure given below shows the displacement and time, $(x-t)$ graph of a particle moving along a straight line: The correct statement, about the motion of the particle, is:

Accepted Answer

1.  **Interpret Slope:** The slope of a displacement-time ($x-t$) graph represents the velocity of the particle ($v = \frac{dx}{dt}$) .
2.  **Analyze Phase 1 (0 to $t_0$):** If the graph is a straight line inclined to the time axis (implied by the correct option describing 'constant velocity'), the slope is constant and non-zero. This indicates uniform motion (constant velocity).
3.  **Analyze Phase 2 (After $t_0$):** If the particle 'stops', its velocity becomes zero. On an $x-t$ graph, zero velocity corresponds to a zero slope, which is a horizontal line parallel to the time axis. The position $x$ remains constant as time increases .
4.  **Conclusion:** The graph describes a particle moving with uniform velocity until $t_0$ and then coming to rest.

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