00:01
In this question, we are given two position functions, and in the first case, we are asked to determine to find the particle's acceleration at the time when its velocity is zero.
00:13
First, we need to find the particle's velocity function.
00:17
V of t equals to x prime of t, and x prime of t in our case equals to cost t plus sine t.
00:27
And now we want to find the values of t when this is zero.
00:34
Words we want cost t to be equal to negative sine t and therefore after dividing both sides by cost t we are going to get that 1 equals to negative sine t over cost t and sine t over cos sine over cos sine over cost is tangent so we're going to get negative tangent t equals to 1 and therefore tangent t equals to negative 1 and tangent t is negative 1 if t is equals to 3 pi over 4, 7 pi over 4, and so on.
01:27
And the first value is 3 pi over 4.
01:31
So t0 equals to 3 pi over 4.
01:35
And now we want to find the particles acceleration at that point.
01:39
We want to calculate a of 3 pi over 4...