 Angular velocity, Angular acceleration
Question

# The position vector of a particle $\stackrel{\to }{R}$ as a function of time is given by $\stackrel{\to }{R}=4\mathrm{sin}\left(2\pi t\right)\stackrel{^}{i}+4\mathrm{cos}\left(2\pi t\right)\stackrel{^}{j}$Where R is in meters, t is in seconds and  denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

Moderate
Solution

## The velocity of the particle is$\stackrel{\to }{v}=\frac{d\stackrel{\to }{R}}{dt}=\frac{d}{dt}\left[4\mathrm{sin}\left(2\pi t\right)\stackrel{^}{i}+4\mathrm{cos}\left(2\pi t\right)\stackrel{^}{j}\right]$$=8\pi \mathrm{cos}\left(2\pi t\right)\stackrel{^}{i}-8\pi \mathrm{sin}\left(2\pi t\right)\stackrel{^}{j}$its magnitude is$|\stackrel{\to }{v}|=\sqrt{\left(8\pi \mathrm{cos}\left(2\pi t\right){\right)}^{2}+\left(-8\pi \mathrm{sin}\left(2\pi t\right){\right)}^{2}}$$=\sqrt{64{\pi }^{2}{\mathrm{cos}}^{2}\left(2\pi t\right)+64{\pi }^{2}{\mathrm{sin}}^{2}\left(2\pi t\right)}$$=\sqrt{64{\pi }^{2}\left[{\mathrm{cos}}^{2}\left(2\pi t\right)+{\mathrm{sin}}^{2}\left(2\pi t\right)\right]}$$=\sqrt{64{\pi }^{2}}$                                       $=8\pi \mathrm{m}/\mathrm{s}$

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