Question

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 8.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed asθ = 2.40t² - 0.750t³ whereθ is in radians and t is in seconds. What is the angular position of the roller at t = 5 seconds?

Answer 1

The angular position of the roller at t = 5 seconds is -33.75 radians.

Step-by-step explanation:

To find the angular position of the roller at t = 5 seconds, we can substitute t = 5 into the given equation: θ = 2.40t² - 0.750t³.

θ = 2.40(5)² - 0.750(5)³

θ = 2.40(25) - 0.750(125)

θ = 60 - 93.75

θ = -33.75 radians.

Therefore, the angular position of the roller at t = 5 seconds is -33.75 radians.