Match Column-I with Column-II : Column-I (x-t graphs) Column-II...

(A) Here, the slope $\dfrac{dx}{dt} \ge 0$ is always increasing, and we know that the derivative graph of the parabola is straight line, so the graph of velocity-time is straight line with increasing slope.

$( A - II )$

(B) Here, the slope $\dfrac{dx}{dt} < 0andatt \to \infty , \dfrac{dx}{dt} \to 0$. As the slope is decreasing with time, so the graph of velocity-time will have negative velocity and positive slope.

$( B - IV )$

(C) Here, the slope $\dfrac{dx}{dt} > 0forfirsthalfand\dfrac{dx}{dt} < 0forsecondhalf$.

As the slope of displacement-time is positive constant in first half and negative constant in second half, so the velocity will be uniform positive and uniform negative value.

$( C - III )$

(D) Here, the slope $\dfrac{dx}{dt} = constant$.

As the slope of displacement-time is positive constant, so the velocity will be uniform positive value.

$( D - I )$