Answer:
Explanation:
Given
[tex]\omega =13-\frac{1}{2}\cdot t^2[/tex]
Motor reverse its direction when \omega =0
[tex]13-0.5t^2=0[/tex]
[tex]26=t^2[/tex]
[tex]t=\sqrt{26}=5.099\approx 5.1 s[/tex]
(b)
[tex]\frac{\mathrm{d} \theta }{\mathrm{d} t}=\omega [/tex]
[tex]\int d\theta =\int_{0}^{5.1}\omega dt[/tex]
[tex]\int d\theta =\int_{0}^{t}(13-.05t^2)dt[/tex]
[tex]\theta =(13t-0.1667\times t^3)_0^{5.1}[/tex]
[tex]\theta =44.192^{\circ}[/tex]
