Find the angular speed at t=3 seconds

[Neon32]

Homework Statement

A shaft is turning at 65.0 rad/s at time zero. Thereafter, its angular acceleration is given by α = -10 rad/s 2 - 5t rad/s 3 where t is the elapsed time. (a) Find its angular speed at t = 3.00 s. (b) How far does it turn in the 3.00 s seconds?

t=3 seconds
wi= 65.0 rad/s
α = -10 rad/s 2 - 5t rad/s 3

Homework Equations

Wf=Wi+αt where α is the angular acceleration

The Attempt at a Solution

since α = -10 - 5t (1)
at t= 3 seconds
by substitution in (1):
α= -25 rad/s2

From Kinematic equation:
wf=wi+αt
wf=65-25(3)= -10 rad /sI found a different answer in the solutions so please tell me why my answer is incorrect.

 

[TSny]

Looks like you tried to solve it by using an equation restricted to constant angular acceleration. Is the angular acceleration constant in this problem? You calculated α at t = 3 s, but that's not the angular acceleration at other instants of time between t = 0 and t = 3 s.

 

[Neon32]

Looks like you tried to solve it by using an equation restricted to constant angular acceleration. Is the angular acceleration constant in this problem?

Yes it isn't constant. So basically i can't use kinematic equations if the acceleration isn't constant??

 

[cnh1995]

Yes it isn't constant. So basically i can't use kinematic equations if the acceleration isn't constant??

Yes. You need to use differential equations w.r.t. time.

 

[Neon32]

Yes. You need to use differential equations w.r.t. time.

Alright. Thanks both of you for the help. Appreciated :)