A particle moves in x-y plane. The position vector of particle at any time t is r = (2 t ) i + (2 t ^ 2 ) j m . The rate of change of at time t = 2 second. (where is the angle which its velocity vector makes with positive x-axis) is

A particle moves in x-y plane. The position vector of particle at any time t is r = (2 t…

Physics · JEE Advanced · NTA Exams — Kinematics

A particle moves in x-y plane. The position vector of particle at any time t is \(\overline{\mathbf{r}}=\left\{(2 \mathrm{t}) \hat{\mathrm{i}}+\left(2 \mathrm{t}^{2}\right) \hat{\mathrm{j}}\right\} \mathrm{m} .\) The rate of change of \(\theta\) at time t = 2 second. (where \(\theta\) is the angle which its velocity vector makes with positive x-axis) is

\(\frac{2}{17} \mathrm{rad} / \mathrm{s}\)
\(\frac{1}{14} \mathrm{rad} / \mathrm{s}\)
\(\frac{4}{7} \mathrm{rad} / \mathrm{s}\)
\(\frac{6}{5} \mathrm{rad} / \mathrm{s}\)

Answer

(A) 2 17 rad / s

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A particle moves in x-y plane. The position vector of particle at any time t is r = (2 t…

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