Figure shows the graph of acceleration a and velocity v on the log-log scale. Which of the following graphs represent the plot of displacement s and velocity v on log-log scale. (Assume the initial velocity to be zero?

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lo g a = 2 1 ​ lo g v ⇒ a = v 1/2 ⇒ d s v d v ​ = v 1/2 ⇒ ∫ v 1/2 d v = ∫ d s ⇒ 3/2 v 3/2 ​ = s ⇒ v 3/2 = 2 3 ​ s ⇒ 2 3 ​ lo g v = lo g 2 3 ​ + lo g s ⇒ lo g s = 2 3 ​ lo g v − lo g 2 3 ​ This represents a straight line with a slope of 2 3 ​ and an intercept of − lo g 2 3 ​ .

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