Changing angular acceleration of a shaft

[jmf322]

Hello, I'm stuck on this problem and I think its because I am lacking the calculus to get the correct answer.

A shaft is turning at 65 rad/s at time = 0. After, its angular acceleration is given by:

a= -10.0 rad/s^2 - 5.00t rad/s^3 where t is the elapsed time.

Find its angular speed at 3 seconds.

Now where I am stuck is I can find its acceleration at 3 seconds, but I believe I need to take the deritive of something in order to calculate the small sections of a/t. Am I on the right track? Any good links to explain how to take the deriitive of a angular acceleration? Thanks!

 

[Cyrus]

if: a=-10-5t

then the velocity is the integral of this function, so, integrate this to find the velocity,

but remember your constant of integration! so you will have a function something like this,

V= - at - 1/2 bt^2 + C C is a constant of integration,

you already know what this value SHOULD be though, because they told you the speed at time 0 is 65. So you have to solve such that 65= - at - 1/2 bt^2 + C ,when time t is zero, this will tell you what C is.

Now you have your general equation, and you just plug in 3 for time to get your angular speed. But ill leave finding a and b to you. it should look similar though.

 

[jmf322]

thanks for the help! Do you or anyone else know of any good calclus with physics applications help site? I understand the Physics in my class, but i struggle with the calculus and calculus web sites are very broad. Thanks again!