00:01
Hi, in this question we are given with the value of angular velocity as 2t square.
00:05
So 2 into t square rad per second and we have r dot which is the linear velocity that is 4t square meter per second.
00:15
So first let us find theta.
00:17
So theta will be integration of 2t square into dt.
00:20
So theta will be 2 into t cube by 3 plus c1 where c1 is the constant of integration.
00:26
Applying initial condition we have t is equal to 0, theta will be equal to 0.
00:31
This implies c1 is 0.
00:33
Therefore theta will be equal to 2 into t cube divided by 3.
00:38
Now we have, so we are given with theta as 45 degree which is pi by 4.
00:44
Therefore t will be equal to, so here t cube will be equal to this is pi by 4, 3 divided by 8 pi or the time will be equal to 1 .056 seconds.
01:02
Then in the next part we have, so here linear velocity is given as 4t square meter per second and we have t value as 1 .056 seconds.
01:15
So r dot will be equal to 4 into 1 .056 whole square.
01:20
So we have velocity v as, so v is 4 .46 meter per second...