00:01
In this problem, we have been given that there is an object and this object gets displaced from the position s -not to s.
00:13
And here we need to show that the displacement of this object, that's s -minus s -not, that is given by the expression v -0 -t plus half -a -t2, provided that the object gets displaced from s -not to s with uniform acceleration.
00:31
So the acceleration is given us constant and we not that's the starting speed.
00:37
So it's the initial speed here.
00:39
So in order to prove this, we know that the acceleration, it is the rate of change of velocity.
00:46
So that's dv by dt.
00:48
And we can just take this dt to the left side.
00:52
So we get dv as a times dt.
00:55
And also we know that the velocity is it's the rate of change of displacement.
00:59
So we can take d t from the right hand side to the left hand side and we can get d s as v times d t.
01:08
So if we integrate this, we're going to get we within the limit, we not to v as a times t.
01:19
And that's going to get us we as v0 plus a t...