Question

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 9.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as θ = 2.90t² - 0.500t³. What is the angular position of the roller at time t?

Answer 1

The angular position of the roller at time t is given by the equation θ = 2.90t² - 0.500t³; substitute the time into the equation to get the angular position in radians.

Step-by-step explanation:

The question is asking to determine the angular position of a cylindrical roller in a manufacturing process at any given time t. The given equation for angular position is θ = 2.90t² - 0.500t³, which is a function of time, where θ is the angular position in radians, and t is the time in seconds.

To find the angular position at any time t, simply substitute the value of t into the equation. For example, at time t = 5 seconds, the angular position would be θ = 2.90(5²) - 0.500(5³) = 2.90(25) - 0.500(125) = 72.5 - 62.5 = 10 radians.