Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.
$(1)$ Velocity decreases $(a)$ Linear graph (constant slope) $(2)$ Velocity increases $(b)$ Concave up graph (increasing slope) $(3)$ Velocity is constant $(c)$ Concave down graph (decreasing slope)
| $(1)$ Velocity decreases | $(a)$ Linear graph (constant slope) |
| $(2)$ Velocity increases | $(b)$ Concave up graph (increasing slope) |
| $(3)$ Velocity is constant | $(c)$ Concave down graph (decreasing slope) |
(A) The slope of a distance-time $(d-t)$ graph represents the velocity of the object.
$(1)$ Velocity decreases: This corresponds to a concave down curve where the slope decreases with time. This matches graph $(c)$.
$(2)$ Velocity increases: This corresponds to a concave up curve where the slope increases with time. This matches graph $(b)$.
$(3)$ Velocity is constant: This corresponds to a straight line with a constant slope. This matches graph $(a)$.
Therefore,the correct matching is $(1-c, 2-b, 3-a)$.
$(1)$ Velocity decreases: This corresponds to a concave down curve where the slope decreases with time. This matches graph $(c)$.
$(2)$ Velocity increases: This corresponds to a concave up curve where the slope increases with time. This matches graph $(b)$.
$(3)$ Velocity is constant: This corresponds to a straight line with a constant slope. This matches graph $(a)$.
Therefore,the correct matching is $(1-c, 2-b, 3-a)$.
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