Kinematics

JEE Main level, single correct, medium

137 of 308

Question 137 of 308

A particle located at x=0x=0 at time t=0t=0, starts moving along the positive xx-direction with a velocity ' vv ' that varies as v=αxv=\alpha \sqrt{x}. The displacement of the particle varies with time as

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Answer: (B) t2t^2

dxdt=α∫dxx=∫αdt⇒xαt2\frac{\mathrm{d} x}{\mathrm{dt}}=\alpha \int \frac{\mathrm{dx}}{\sqrt{\mathrm{x}}}=\int \alpha \mathrm{dt} \Rightarrow \mathrm{x} \alpha \mathrm{t}^2

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