00:01
In this question, we are asked to find the velocity and position vectors of the particle with a given acceleration and given initial velocity of position.
00:10
To find the v of t, we need to integrate a of t.
00:16
To integrate a of t, we simply need to integrate each coordinate of the function a.
00:36
The first interval leads to 3t squared plus e to the t plus the constant of integration c.
00:46
And the second one leads to 12 t cube over 3 plus another constant of integration d.
01:01
We have to be careful here.
01:02
We need to use different constants of integration because these are different intervals.
01:09
And this equals to 3t squared plus e to the t plus c times i, plus 4t cube plus d times j.
01:26
Now we need, that's v of t right, that's the velocity function.
01:31
Now we need to find the constants of integration.
01:33
And to do that, we will use this condition.
01:38
V of 0 equals to 3i.
01:41
But we can rewrite that as 3i plus 0 j right...