00:01
We're told that the speed of a particle, its velocity, is negative 0 .4 t to square second plus 6t.
00:08
And we're told that it's in meters per second.
00:12
The first part is asking, how far does the particle travel during the first three seconds? well, to answer that, we first need to find the position of the particle.
00:24
Well, position is just the integral of velocity.
00:27
So i'm going to integrate t squared is t cubed.
00:31
And then i have to divide by 3.
00:34
So i get negative point 4 over 3 t cubed plus integral of t is t squared, but then i divide by it, 6 over 2 is 3.
00:45
And it starts at position 0.
00:48
So i'm just going to say plus 0.
00:51
That's it.
00:53
So for part a, i just need to take s of 3.
00:58
That's position it was at time 3 and subtract.
01:04
The position at time 0...