00:01
So in this question, i say i have a particle and it moves along the x -axis with an acceleration given by a of t equals 6t plus 2, where t is measured in seconds and my position is measured in meters.
00:15
If the initial position is given by s of 0 equals 3 and the initial velocity is given by v of 0 equals 4, i want to find the position of the particle at t seconds.
00:27
So they've given me my acceleration, and i want to get back to my position.
00:33
To start, i know that velocity is the antiderivative of acceleration.
00:41
So i know that my velocity is the anti -derivative of 6t plus 2 dt.
00:51
My anti -derivative of 6t plus 2 is going to be 3t squared plus 2 t plus 2t plus a constant now they told me my velocity at times zero is 4.
01:06
So by substitution, my v of 0 is 0 plus 0 plus c.
01:13
Since v of 0 was 4, 4 is equal to my c.
01:19
And so this implies that my velocity is 3t squared plus 2t plus 4.
01:28
Now, to get my position, i know that position is the antiderivative of my velocity...