Answer :
Answer:
The angular acceleration and angular displacement is [tex]-2.24\ m/s^2[/tex] and 31.34 rad .
Explanation:
Given :
Initial linear speed , u = 9.8 m/s .
Final speed , v = 2.2 m/s .
Time taken , t = 3.4 s .
Radius of wheel , r = 0.65 m .
So , decelerates of wheel is given by :
[tex]v-u=at\\2.2-9.8=a\times 3.4\\a=-2.24\ m/s^2[/tex]
Therefore , angular velocity is given by :
[tex]\omega=\dfrac{a}{r}\\\\\omega=\dfrac{-2.24}{0.65}\\\\\omega =-3.45\ rad/s^2[/tex]
Now , linear displacement is :
[tex]s=ut+\dfrac{at^2}{2}\\\\s=9.8\times 3.4+\dfrac{-2.24\times 3.4^2}{2}\\\\s=20.37\ m[/tex]
Therefore , angular displacement is :
[tex]d=\dfrac{s}{r}\\\\d=\dfrac{20.37}{0.65}\\\\d=31.34\ rad[/tex]
Hence , this is the required solution .