00:01
Alright, so now in this problem a particle is moving with the given data, find the position of the particle s of t.
00:09
So here a of t is given to us which is equal to t square minus 8t plus 3, right.
00:17
Also it is given s of 0 is equal to 0, s of 1 is equal to 20.
00:24
So this is given values, right.
00:26
Now we need to find out s of t, right.
00:31
So what we know about the acceleration, 8t means acceleration which is differentiation of velocity that is divided by dt, right.
00:45
Also vt is and, so this is, this is key concept we have to understand.
00:55
So there is a relation between acceleration 8t and vt and vt has relation with s t which is differentiation of distance, right.
01:06
So simple as that.
01:08
So now we are given with 8t.
01:11
So that means we need to integrate it then only we will be getting 8t.
01:15
Therefore vt would be equals to integration of 8t dt.
01:22
So this is a, this is an indefinite integral, right.
01:29
So it becomes t square minus 8t plus 3, right.
01:35
So dt here, okay.
01:38
So now this becomes equals to t cube by 3 after integration.
01:48
Now this is 8t square by 2 plus 3t plus c1 let us say.
01:56
So this is the value of vt now.
02:00
Now what happens is we know to find s t, to find s t, what we do is we will integrate vt, right, with respect to t, like t, dt you can say, right.
02:19
The variable is t here.
02:21
So now again it will be t to the power 4 that will be divided by 4, 4 trees are 12, right.
02:28
So here it will be 2 to the, 2 4s are 8, right.
02:35
So that means it becomes 4t cube by 3 here plus we have 3t square by 2 plus c1t, correct.
02:49
Now plus c2, right.
02:52
So this is the value for s t, right.
02:56
So simple.
02:57
But we don't know the value of c1t, c1 and c2.
03:06
So what will be s0 now, when you put t is equals to 0, you will be getting this will be 0, this will be 0 plus this will be 0.
03:15
Now we are left with c1 multiplied by 0, this is 0 plus c2, right...