00:01
Determine the magnitude of the velocity of point a when t is equal to 2 seconds.
00:07
So we need to integrate our angular speed.
00:10
We can integrate from, we're given our initial omega naught, so we're integrating from 14 to omega of d omega, and set that equal to our integral from 0 to 2 of 3t squared plus 11 dt.
00:27
We find omega minus 14 is equal to t cubed plus 11t, evaluated from 0 to 2.
00:39
So when this is 0, we get nothing, but we can rewrite omega minus 14 is equal to 2 cubed plus 11 times 2, so we just add 14 to get omega.
00:52
So we can go ahead and plug that in.
00:54
We have 2 cubed plus 11 times 2 plus 14, we get 44.
01:03
And now we want to find our velocity.
01:06
We find velocity at point a is equal to our radius at point a times omega.
01:12
Our radius at point a is 0 .5 meters, so we multiply 0 .5 by 44, and we get 22 meters per second.
01:22
Now for b, we'd like to find the magnitudes of the n and t components of the acceleration...