00:01
In this exercise, we have that, after analyzing the route of a nave extraterrestrial, has been found that your position in function of the time can be recrited by the next equation.
00:11
So, the position in function of the time is equal to 2, more 3 for the time to the 4, and this more 4 for the time to to the 3, this in the direction x, and in the direction y, we have three, more four times the time, more five times the time, or the time, or the and this in the direction y.
00:56
Now, the question is, what are the velocity and the acceleration of the nav in function of the time? so, we have to find the velocity and the acceleration of the nav in function of the time.
01:11
To find this first part, we know that the velocity in function of the time is the derivative of the position in function of the time with respect to the time.
01:22
So what we need to do now is simply simply to take the derivative, of the expression that is then we start we'll with the coordinate in x we know that the derivative of a constant is zero the derivative of the time to allow the 4 the exponent that would 3 for 4 for the time to the 3 then would 12 for the time to 3 more the time at 3 we'll we'll we'll 3, and 4x3, 12, for the time to quadrador.
02:03
And this in the direction x, and now we pass to the direction y.
02:07
Of new, we know that the derivative of a constant is 0.
02:11
The derivative of the time with respect to the time is simply one.
02:15
So, it would 1 .4, 4, 4, more, here we have two times in the derivative of the time to quadrador, that is two times the time for 5, would 10 times the time, this, in the coordinate y.
02:31
And now, to obtain the acceleration, we know that that is the first derivative of the velocity with respect to the time, or also we could have to be the second derivative of the position with respect to the time.
02:45
Now, as we've got the velocity, with respect to the time, we'll reach the acceleration.
02:53
Then, we start with the first term.
02:55
Here the exponent and it would 12 for 3 that is 36 times the time to quadrado more 2 for 12 is 24 for the time this in the position x more of new here we have one constant so derivative is 0 and the derivative of the time with respect to the time is simply one for what we obtain 10 and this is the the solution for the first part of this problem.
03:29
Now, we're going to calculate the magnitude of the vector velocity and the vector acceleration for a time, for the time, equal to four seconds.
03:42
So we'll start with the velocity...