A wheel starts from rest and has an angular acceleration that is given by α(t) = (6rad/s^4)t^2 , The angle through which it turns in time t is given by ?

I have got the answer 3t^4 , but the answer was (.5)t^4 !

Question

A wheel starts from rest and has an angular acceleration that is given by α(t) = (6rad/s^4)t^2 , The angle through which it turns in time t is given by ?

I have got the answer 3t^4 , but the answer was (.5)t^4 !

anonymous · Answer

how did you get that?

the answer is (.5)t^4... can you show me the work?

anonymous · Answer

i mean show me your work.. so ll tell where yu went wrong

anonymous · Answer

ok i got what you did.. and thats wrong.. you used the equation of motion.. that only works of the acceleration is a constant.. here.. the acceelration is clearly not a  constant.. depends on time t.. hence you need to integrate!

fifciol · Answer

integrate twice your a(t) function. you will get:
$$\int\limits_{}^{}6t^2dt=2t^3$$
$$\int\limits_{}^{}2t^3dt=0.5t^4$$

anonymous · Answer

don't give out direct answers mate.. let him think ;-)!

anonymous · Answer

@Mashy  ,, yes that right i made that mistake !

anonymous · Answer

yea so now you know right? :)

fifciol · Answer

ok @Mashy  :)

anonymous · Answer

@Mashy  ,, ,, yes I had known it :) thanx
@Fifciol ,, Thank you too