The displacement of a particle travelling along the X-axis is shown...

The force acting on a particle is zero when its acceleration is zero ($F = ma$).

Acceleration is the second derivative of displacement with respect to time ($a = \dfrac{d^2x}{dt^2}$). On a displacement-time ($x-t$) graph, acceleration is zero when the slope of the graph (velocity) is constant, which corresponds to a straight line.

From the given graph, the segments $AB$ and $CD$ are straight lines. This indicates that the velocity is constant in these regions.

Therefore, the acceleration is zero, and the force acting on the particle is zero in regions $AB$ and $CD$.

In regions $BC$ and $DE$, the graph is curved, indicating a changing slope (changing velocity), so the acceleration and force are non-zero.