The velocity-time graph for a particle moving | vedclass

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(D) The velocity-time $(v-t)$ graph shows that the velocity increases linearly from $0$ to a maximum value $v$ in the first interval,indicating consta

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(D) The velocity-time $(v-t)$ graph shows that the velocity increases linearly from $0$ to a maximum value $v$ in the first interval,indicating constant positive acceleration. For a constant positive acceleration,the displacement-time $(x-t)$ graph must be a parabola opening upwards $(x \propto t^2)$. In the second interval,the velocity is constant and negative,which means the particle moves with a constant negative velocity. For constant negative velocity,the $x-t$ graph must be a straight line with a negative slope. Comparing this with the given options,the graph that shows a parabolic increase followed by a straight-line decrease is represented by option $D$.

The velocity-time graph for a particle moving along the $x$-axis is shown in the figure. The corresponding displacement-time graph is correctly shown by

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