A particle located at x = 0 at time...
Question

# A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity that varies as v = a (x. The displacement of the particle varies with time as (AIEEE-2006] (C) t (D) 1/2 (A) 3 (B) 12

JEE/Engineering Exams
Physics
Solution
125
4.0 (1 ratings)
[ begin{array}{l}v=a sqrt{2} cdot sqrt{x} Rightarrow int_{0}^{x} x^{-1 / 2} d x=int a d 1 frac{d x}{d x}=a sqrt{frac{x^{1 / 2}}{1 / 2}} int_{0}^{x}=a[t]_{0}^{t}end{array} ] ( begin{array}{ll}Rightarrow quad 2 sqrt{x}=text { at } Rightarrow frac{4 x}{x}=frac{a^{2} t^{2}}{4} & Rightarrow frac{a^{2} t^{2}}{4}end{array} )