A particle located at x = 0 at time...
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A particle located at x = 0 at time t=0.starts moving along the positive x-direction with a velocity v 'which varies as v= avx, then velocity of particle varies with time as: (a is a constant)

JEE/Engineering Exams
Physics
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( frac{d x}{d x}=alpha sqrt{x} ) ( Rightarrow frac{d x}{sqrt{x}}=2 d t ) ( Rightarrow int x^{-1 / 2} d x=int alpha d t ) ( Rightarrow quad 2 sqrt{x}=alpha eq+c ) at ( t=0, n=0 Rightarrow c=0 ) ( Rightarrow 2 sqrt{x}=alpha t ) ( Rightarrow quad x=frac{alpha^{2} t^{2}}{4} ) ( Rightarrow frac{d x}{d t}=V=frac{alpha^{2} t}{2} ) ( a=frac{d v}{d t}=frac{alpha^{2}}{2} cdot ) constant
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