A particle moves in a circle of radius $R$, with a constant speed $v$. Then, during a time interval $\left[\frac{\mathrm{\pi R}}{3v}\right]$, which of the following is true?

 

 

 

 

 

$\begin{array}{r}\mathrm{T}=\frac{2\pi l}{\mathrm{v}}\mathrm{t}=\frac{\mathrm{T}}{6} \\ \theta =\frac{\pi }{3} \\ \mathrm{\Delta V}=\sqrt{2{\mathrm{v}}^2-2{\mathrm{v}}^2\cos \pi /3}=\mathrm{v} \\ {\mathrm{a}}_{\mathrm{avg}}=\frac{\mathrm{v}}{\mathrm{T}/6}=\frac{6\mathrm{v}}{2\pi \mathrm{R}}=\frac{3{\mathrm{v}}^2}{\pi \mathrm{R}} \\ {\mathrm{v}}_{\mathrm{avg}}=\frac{\mathrm{R}}{\mathrm{T}/6}=\frac{6\mathrm{Rv}}{2\pi \mathrm{R}}=\frac{3\mathrm{v}}{\pi } \end{array}$