Match Column-I with Column-II : Column-I (x-t graphs) Column-II (v-t graphs) A I B II C III D IV Choose the…

(A) Here, the slope $\frac{\mathrm{d}x}{\mathrm{d}t}\ge 0$ 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 $\frac{\mathrm{d}x}{\mathrm{d}t}<0 \mathrm{and} \mathrm{at} t\to \infty ,\frac{\mathrm{d}x}{\mathrm{d}t}\to 0$. 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 $\frac{{\displaystyle \mathrm{d}x}}{{\displaystyle \mathrm{d}t}}>0 \mathrm{for} \mathrm{first} \mathrm{half} \mathrm{and} \frac{{\displaystyle \mathrm{dx}}}{{\displaystyle \mathrm{dt}}}<0 \mathrm{for} \mathrm{second} \mathrm{half}$.

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 $\frac{{\displaystyle \mathrm{d}x}}{{\displaystyle \mathrm{d}t}}=\mathrm{constant}$.

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

$(D - I)$