A particle moves such that its position vector r (t)= t i + t j where is a constant and t…

Physics · NEET · NTA Exams — Kinematics

A particle moves such that its position vector \(\vec{r}(t)=\cos \omega t \hat{i}+\sin \omega t \hat{j}\) where ω is a constant and t is time. Then which of the following statements is true for the velocity \(v(t)\) and acceleration \(\vec{I}(t)\) of the particle:

\(\overrightarrow{\mathbf{V}}\) is perpendicular to \(\overrightarrow{\mathrm{r}}\) and \(\overrightarrow{\mathrm{Z}}\) is directed towards the origin
\(\overrightarrow{\mathbf{V}}\) and \(\overrightarrow{\mathrm{Z}}\) both are parallel to \(\overrightarrow{\mathrm{r}}\)
\(\overrightarrow{\mathbf{V}}\) and \(\overrightarrow{\mathrm{Z}}\) both are perpendicular to \(\overrightarrow{\mathrm{r}}\)
\(\overrightarrow{\mathbf{V}}\) is perpendicular to \(\overrightarrow{\mathrm{r}}\) and \(\overrightarrow{\mathrm{Z}}\) is directed away from the origin

Answer

(A) V is perpendicular to r and Z is directed towards the origin

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A particle moves such that its position vector r (t)= t i + t j where is a constant and t…

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