Answer :
Answer:
225 rpm
Explanation:
The angular acceleration of the fan is given by:
[tex]\alpha = \frac{\omega_f - \omega_i}{\Delta t}[/tex]
where
[tex]\omega_f[/tex] is the final angular speed
[tex]\omega_i[/tex] is the initial angular speed
[tex]\Delta t[/tex] is the time interval
For the fan in this problem,
[tex]\omega_i = 0\\\omega_f = 180 rpm\\\Delta t=4 s[/tex]
Substituting,
[tex]\alpha = \frac{180-0}{4}=45 rpm/s[/tex]
Now we can find the angular speed of the fan at the end of the 5th second, so after t = 5 s. It is given by:
[tex]\omega' = \omega_i + \alpha t[/tex]
where
[tex]\omega_i = 0\\\alpha = 45 rpm/s\\t = 5 s[/tex]
Substituting,
[tex]\omega' = 0 + (45)(5)=225 rpm[/tex]