How long would it take Exena to close the door if she doubled the magnitude of the force applied to the door

  y /y₀ = 1 /√2 = 0.70

Explanation:

To close the door, a torque must be applied in such a way that there is an angular acceleration and after a period of time the angle of the door moves.

If the force is doubled keeping the other parameters without altering angular acceleration is

                 F r = I α

                 α = F r / I

if we double the force

           α = 2F r / I

            α=2 α₀

let's use the angular kinematics relations

            θ = w₀ t + ½ α t²

we assume the door was still before pushing it

            θ = ½ a t²

            t = √ (2θ / a)

as we saw the angular acceleration is double

            t = √ (2θ / 2a₀)

            t = 1 / √2  a₀

the relationship between the two times is

            y /y₀ = 1 /√2 = 0.70

This time that has been reduced closes the door.

think about the oscillation of the toy shown in the video. when the toy is at the highest point of its motion, its velocity is zero and its acceleration is negative.

explanation:

wheres the pic