00:01
Hello students, here it is given that an object moving along the line with a velocity v of t where the given velocity is v of t equal to 9 cos pi t where t lies between 0 to 2 where t is measured in seconds.
00:24
First we have to determine when the motion is in the positive direction and when it is in the negative direction such that we know states that the motion is in the positive direction when the velocity is positive and the motion is in the negative direction when the velocity is negative.
00:43
So that here we have to equate the velocity to 0 such that here v of t is 9 cos pi t which is equal to 0 such that we can say pi t equal to cos inverse of 0.
00:59
We know cos inverse of 0 is pi by 2.
01:02
We can generalize it that is pi t equal to 2 n plus 1 pi by 2.
01:11
Therefore t will be 2 n plus 1 by 2.
01:16
Here we have to find the time and the velocity for n equal to 2 for n equal to 0 t will be 1 by 2.
01:35
Then we have to find the velocity at that point.
01:39
Therefore velocity at 1 by 2 is 9 cos of pi by 2.
01:48
We know cos pi by 2 is 0.
01:49
Therefore v of t equal to 0 and for n equal to 1 and for n equal to 2 we have the following.
02:00
Here for n equal to 0 t equal to 1 by 2 and v of 1 by 2 is 0 and for n equal to 1 t will be 3 by 2 and the velocity at 3 by 2 is 0...