An automatic dryer spins wet clothes at an angular speed of 5.8 rad/s. Starting from rest, the dryer reaches its operating speed with an average angular acceleration of 3.3 rad/s². How long does it take the dryer to come up to speed?

[tex]\begin{gathered} \omega_f=\omega_i+\alpha t \\ where \\ \omega_f\text{ is the final angular speed} \\ \omega_i\text{ is the initial angular speed} \\ \alpha\text{ is the angular acceleration} \\ t\text{ is the time} \end{gathered}[/tex]

Step 1

a)let

[tex]\begin{gathered} initial\text{ angular speed= 0\lparen rest\rparen} \\ final\text{ angular speed=5.8}\frac{rad}{s} \\ angular\text{ acceleration=}\alpha=3.3\frac{rad}{s^2} \end{gathered}[/tex]

b) now, replace in the formula and solve for t ( time)

[tex]\begin{gathered} \omega_{f}=\omega_{i}+\alpha t \\ 0\frac{rad}{s}=5.8\frac{rad}{s}+3.3\frac{rad}{s^2}*t \\ 0=5.8+3.3t \\ subtract\text{ 5.8 in both sides} \\ 0-5.8=5.8+3.3t-5.8 \\ -5.8=3.3t \\ divide\text{ both sides by 3.3} \\ \frac{-5.8}{3.3}=\frac{3.3t}{3.3} \\ t=1.7575 \\ (\text{ the negative sign indicates the acceleration is negative, opposite to motion way\rparen} \end{gathered}[/tex]

therefore, the answer is

1.7575 seconds