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Sagot :
First, let's convert the displacement to radians:
[tex]10.9\text{ rev}=10.9\cdot2\pi\text{ rad}=21.8\pi\text{ rad}[/tex]Now, let's calculate the angular acceleration using Torricelli's equation:
[tex]\begin{gathered} V^2=V_o^2+2\cdot a\cdot d\\ \\ 0=13.1^2+2\cdot a\cdot21.8\pi\\ \\ 43.6\pi a=-171.61\\ \\ a=\frac{-171.61}{43.6\pi}\\ \\ a=-1.253\text{ rad/s^^b2} \end{gathered}[/tex]Now, to calculate the time, we can use the formula below:
[tex]\begin{gathered} V=V_o+at\\ \\ 0=13.1-1.253t\\ \\ 1.253t=13.1\\ \\ t=\frac{13.1}{1.253}\\ \\ t=10.45\text{ s} \end{gathered}[/tex]
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