Figure shows the x-t plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t > 0 ? If not, suggest a suitable physical context for this graph.

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Solution

The position-time graph is used to determine the position of the body at any instant but not for determining the trajectory of the body.

At the time $t < 0$
x = const.
it means that the particle is at rest

whereas, for $t > 0$
$x = k t^{2}$ (parabola)
It moves in straight line, it is a 1d motion.

Context: A body is dropped from a tower (x = 0) at t = 0.

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