frequency of engine is given here
[tex]initial frequency = 1200 rpm[/tex]
[tex]f_i = 1200/60 = 20 Hz[/tex]
[tex]final frequency = 3000 rpm[/tex]
[tex]f_f = 3000/60 = 50 Hz[/tex]
now we have angular speed as
[tex]\omega_i = 2\pi f_i [/tex]
[tex]\omega_i = 2\pi(20) = 40\pi[/tex]
similarly
[tex]\omega_f = 2\pi f_f[/tex]
[tex]\omega_f = 2\pi(50) = 100 \pi[/tex]
now by the formula of angular acceleration we will have
[tex]\alpha = \frac{\omega_f - \omega_i}{\Delta t}[/tex]
[tex]\alpha = \frac{100\pi - 40\pi}{3}[/tex]
[tex]\alpha = 20\pi rad/s^2[/tex]
[tex]\alpha = 62.8 rad/s^2[/tex]
