00:01
In this question, we are asked to find the position of a particle satisfying the given conditions.
00:07
To do that, we'll first rewrite these vectors using component form.
00:13
The acceleration equals negative 3 sine 3t and negative 3 cos 3t.
00:26
R dot velocity at 0 equals 1 0 and the position at 0 equals negative 3 3.
00:38
Now it will be easier to do the calculations.
00:41
To find the velocity function, we need to integrate the acceleration function.
00:48
To integrate the acceleration function, we need to integrate each coordinate.
00:55
The integral of negative 3 sine 3t equals negative 3 times negative 1 3rd cos 3t.
01:05
And since this is an indefinite integral, there will be a constant of integration c1.
01:11
The integral of negative 3 cos 3t equals negative 3 times 1 3rd sine 3t plus another constant of integration c2.
01:25
And this simplifies to cos 3t plus c1 and negative sine 3t plus c2.
01:46
Now let's calculate this at 0...