Answer:
R = 7.06 m
Explanation:
As we know that time period of the particle is T = 1 s
so the angle covered by it in t = T/6 seconds is given as
[tex]\theta = \frac{2\pi}{T}t[/tex]
[tex]\theta = \frac{2\pi}{1}\times \frac{1}{6}[/tex]
[tex]\theta = \frac{\pi}{3}[/tex]
now we know that total distance moved by the particle will be
[tex]d = R\theta = R\times \frac{\pi}{3}[/tex]
now average speed is given as
[tex]v = \frac{R\times \frac{\pi}{3}}{\frac{1}{6}}[/tex]
[tex]v = 2\pi R[/tex]
now for displacement of the particle we know that
[tex]\vec d = \sqrt{R^2 + R^2 - 2(R)(R)cos\frac{\pi}{3}}[/tex]
[tex]\vec d = R[/tex]
so average velocity is given as
[tex]\vec v = \frac{R}{\frac{1}{6}} = 6R[/tex]
now we have
[tex]v - \vec v = 2\pi R - 6 R = 2 m/s[/tex]
[tex]R = \frac{2}{2\pi - 6} = 7.06 m[/tex]
