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The angular velocity of a process control motor is (13−12t2) rad/s, where t is in seconds. Part A At what time does the motor reverse direction? Express your answer to two significant figures and include the appropriate units. tt = nothing nothing Request Answer Part B Through what angle does the motor turn between t =0 s and the instant at which it reverses direction? Express your answer to two significant figures and include the appropriate units. ΔθΔ θ = nothing nothing Request Answer

Respuesta :

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]

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