00:01
Hi there, here particle is moving along x -axis and its velocity is described by the function to t squared meters per second.
00:16
So at the initial position when time is zero seconds, x0 is 2 meters.
00:33
And here we have to calculate position at 2 .7 seconds.
00:48
Let's do this.
00:53
So here, the position of the particle equals to the integral of its velocity.
01:11
And here that is integral from 0 to time t, which is which equals to integral of 2t squared d t.
01:35
So let's actually here let's calculate the indefinite integral for now for now.
01:45
We'll convert it to the definite integral.
01:48
So the anti -derivative of this function 2d squared is 2 thirds t -ccccc and plus constant.
02:06
So when time equals to 0 x equals to 2, that's why the function is 2 thirds ccube plus 2 .0 that is in meters.
02:25
So therefore when x equals to 2 .7 seconds x equals to 2 thirds times 2 .7 seconds cubed plus 2 .0 and it's all in meters.
02:50
Let's calculate it...