initial angular speed is given by 33.3 rpm
[tex]w_0 = 2\pi \frac{33.3}{60}[/tex]
[tex]w_0 = 3.49 rad/s[/tex]
final angular speed is given by 78 rpm
[tex]w_f = 2\pi \frac{78}{60}[/tex]
[tex]w_f = 8.17 rad/s[/tex]
now by using kinematics we will have
[tex]w_f = w_0 + \alpha * t[/tex]
[tex]8.17 = 3.49 + 2.15 * t[/tex]
[tex] t = 2.17 seconds[/tex]
