Answer:[tex]t_1\times \frac{1}{5}[/tex]
Explanation:
Given
Motor accelerate motor to angular velocity of [tex]\omega _1[/tex]
angular acceleration [tex]\alpha [/tex]
time taken [tex]t_1[/tex]
thus [tex]\omega _1=0+\alpha t_1[/tex]
At this point brake is applied that decelerate the wheel with angular acceleration [tex]-5\alpha [/tex]
Let us take time taken to be [tex]t_2[/tex]
using
[tex]\omega =\omega _0+\alpha t[/tex]
where [tex]\omega =final\ angular\ velocity[/tex]
[tex]\omega _0=initial\ angular\ velocity[/tex]
[tex]\alpha =angular acceleration[/tex]
[tex]t=time[/tex]
[tex]0=\alpha t_1-5\alpha \cdot t_2[/tex]
[tex]t_2=t_1\times \frac{1}{5}[/tex]
