The velocity (v)-time (t) graph for a particl | vedclass

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(A) The velocity $(v)$ is the slope of the position $(x)$-time $(t)$ graph,i.e.,$v = \frac{dx}{dt}$.In the first interval,the velocity increases linea

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(A) The velocity $(v)$ is the slope of the position $(x)$-time $(t)$ graph,i.e.,$v = \frac{dx}{dt}$.In the first interval,the velocity increases linearly from $0$ to a maximum value. Since $v = at$ (where $a$ is constant acceleration),the position $x = \int v dt = \frac{1}{2}at^2$,which is a parabola opening upwards.In the second interval,the velocity is negative and its magnitude decreases linearly to $0$. This implies a negative acceleration (deceleration). The position $x$ will follow a parabolic path that returns to the initial position (or a specific point) with a decreasing slope.The correct graph shows a parabolic increase in position followed by a parabolic decrease,which matches the shape where the slope of the $x-t$ graph corresponds to the given $v-t$ graph.

The velocity $(v)$-time $(t)$ graph for a particle moving along the $x$-axis is shown in the figure. The corresponding position $(x)$-time $(t)$ graph is best represented by:

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