00:01
Now in this problem we are given that a boat is traveling along a circular path with speed v to be equals to 0 .0625 t square and the radius of this circular arc rho is given to be 45 meter.
00:19
Now we need to find the magnitude of its acceleration at time t equals to 12 second.
00:26
Now here we see that the velocity is changing with respect to time which is given by this.
00:34
So two accelerations will come one is the centripetal acceleration towards the center another one is the tangential acceleration towards the this tangential direction at.
00:47
So two accelerations will come.
00:50
So first let us find the centripetal acceleration.
00:53
So centripetal acceleration is given by v square over r.
00:58
Now here v is this.
01:00
So let's find the velocity at time t equals to 12.
01:04
So velocity at time t equals to 12 would be 0 .0625 multiplied with 12 square and this to be equals to 9 meter per second and r is the radius which is given rho.
01:19
So r is just the rho which is equals to 45 meter.
01:23
Plug it here to find the centripetal acceleration.
01:26
So 9 square divided by 45 which will be equals to 1 .8 meter per second squared...