Can I use this solution? Angular motion

[OrlandoLewis]

Homework Statement

Starting from rest, a wheel has constant α = 3.0 rad/s². During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval?

ω₀ = 0
α = 3.0 rad/s²
θ_f = 120 rad

Homework Equations

Δθ = ω₀⋅t + ½αt²

The Attempt at a Solution

120 rad = (1/2)(3.0 rad/s²)(t²)
Solving for t:
t = [2(120 rad) / (3.0 rad/s^2)]^½
t = 8.49 s
Subtracting 4.0 s to the said time leads to my final answer, 4.9 s

The book says that the answer should be 8.0 s.

 

[Arman777]

It says "during a certain 4.0s interval " it could be between any time interval.Your equation describes us what is the time when it makes 120 rad we are not looking for that,we are looking for a time interval which object makes 120 rad.
Can you see the difference ?

 

[Doc Al]

During the given interval, Δθ = 120 rad. But that's not measured from the starting point.

You found the time it takes to go from the starting point to θ_f = 120 rad, which is a different problem.

Set up two equations.

Edit: Oops, didn't see that Arman777 just said the same thing. :-)

 

[OrlandoLewis]

It says "during a certain 4.0s interval " it could be between any time interval.Your equation describes us what is the time when it makes 120 rad we are not looking for that,we are looking for a time interval which object makes 120 rad.
Can you see the difference ?

It's still pretty vague to me from how you said it. So I'll try to explain as far as I can understand.

At the beginnig it starts to accelerate up to a certain velocity. From that point up to 4 seconds, the said theta is measured until 210 radians.
Is that how I should interpret the problem?

 

[Arman777]

It's still pretty vague to me from how you said it. So I'll try to explain as far as I can understand.

At the beginnig it starts to accelerate up to a certain velocity. From that point up to 4 seconds, the said theta is measured until 210 radians.
Is that how I should interpret the problem?

It made some rad $θ_1$ between $t=0$ and $t_1$,
After 4 sec, which let's call is $t_2$ (or $t_1+4$) it makes $θ_2$ rad (between $t_2$ and $t=0$)
In between those time intervals ($t_2$ and $t_1$) it makes $120$ rad.

 

[haruspex]

It made some rad $θ_1$ between $t=0$ and $t_1$,
After 4 sec, which let's call is $t_2$ (or $t_1+4$) it makes $θ_2$ rad (between $t_2$ and $t=0$)
In between those time intervals ($t_2$ and $t_1$) it makes $120$ rad.

Yes, but I feel it could be expressed yet more clearly.
It accelerates at 3 rad s^-2 from rest for some time t, turning through some angle in the process. Continuing with the same acceleration for another 4 seconds it turns through a further 120 radians. Find t.