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Question

(A) The velocity $v$ is given by the slope of the $x-t$ graph,i.e.,$v = \frac{dx}{dt}$.$(A)$ The $x-t$ graph is a parabola opening upwards,indicating

Vedclass · Accepted Answer

$(A)-(II), (B)-(IV), (C)-(III), (D)-(I)$

Vedclass · Answer

(A) The velocity $v$ is given by the slope of the $x-t$ graph,i.e.,$v = \frac{dx}{dt}$.$(A)$ The $x-t$ graph is a parabola opening upwards,indicating increasing slope. Thus,$v$ increases with time. This matches graph $II$.$(B)$ The $x-t$ graph shows a decreasing position with a decreasing slope (magnitude),approaching zero. This corresponds to a negative velocity whose magnitude decreases towards zero. This matches graph $IV$.$(C)$ The $x-t$ graph shows a constant positive slope followed by a constant negative slope. This corresponds to a positive constant velocity followed by a negative constant velocity. This matches graph $III$.$(D)$ The $x-t$ graph is a straight line with a constant positive slope,indicating constant positive velocity. This matches graph $I$.Therefore,the correct matching is $(A)-(II), (B)-(IV), (C)-(III), (D)-(I)$.

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