Question

The angular velocity of a process control motor is w = (20 - .5t²) rad/s, where t is in seconds. What time does the motor reverse direction?

Answer 1

To find the time when the motor reverses direction, set the angular velocity equation equal to zero and solve for t.

Step-by-step explanation:

To find the time when the motor reverses direction, we need to set the angular velocity equation equal to zero.

Given: ω = 20 - 0.5t² where t is in seconds.

Setting ω equal to zero: 0 = 20 - 0.5t²

Solving for t:

t² = 40

t = ±√40

Since time cannot be negative, the motor reverses direction when t = √40 seconds.