Time at a certain reference line

[bearhug]

At t=0, a flywheel has an angular velocity of 4.7 rad/s, a constant angular acceleration of -0.25 rad/s^2, and a reference line at θ(t=0)=0 rad.
Assuming the motion proceeded similary at times before t=0, at what negative time was the reference line at θ=-10.5 rad?

Based on this question I'm assuming that acceleration is still -0.25 rad/s^2 and angular velocity is still 4.7 rad/s.

Θf = θi + ωit + 1/2αt^2 is the equation I was planning on using to find time. However I'm confused as to what I should consider the final radians and final velocity. Should it be at θ=0 with final velocity at 4.7 rad/s?

 

[OlderDan]

At t=0, a flywheel has an angular velocity of 4.7 rad/s, a constant angular acceleration of -0.25 rad/s^2, and a reference line at θ(t=0)=0 rad.
Assuming the motion proceeded similary at times before t=0, at what negative time was the reference line at θ=-10.5 rad?

Based on this question I'm assuming that acceleration is still -0.25 rad/s^2 and angular velocity is still 4.7 rad/s.

Θf = θi + ωit + 1/2αt^2 is the equation I was planning on using to find time. However I'm confused as to what I should consider the final radians and final velocity. Should it be at θ=0 with final velocity at 4.7 rad/s?

When you write
Θ = θi + ωit + 1/2αt^2
you are effectively saying that α is a constant and that
ω = ωi + αt
So
θi is the value of Θ when t = 0
ωi is the value of ω when t = 0
Putting those values into
Θ = θi + ωit + 1/2αt^2
allows you to find Θ at any other time (positve or negative)

 

[kyle8921]

I would first clarify with the person asking the question whether the flywheel's motion before t=0 followed the same pattern as after t=0. If that is the case, then the equation Θf = θi + ωit + 1/2αt^2 can be used to solve for the time at which the reference line was at θ=-10.5 rad.

However, if the person asking the question is unsure or if there were any changes in the flywheel's motion before t=0, then we cannot assume that the same equation can be used. In this case, more information or clarification is needed to accurately determine the time at which the reference line was at θ=-10.5 rad.