00:01
In this problem, we have a particle that's moving along a straight line, and its position is given by this equation, s is equal to 12 minus 15 t squared plus 5t cubed, and this is all given in meters, and t is the time in seconds.
00:19
And so the questions that are asked of us are to find the average speed of the particle, the average acceleration, a average, and the total distance, delta s, traveled between t equals 1 and t equals 3 seconds.
00:45
Okay, so i'm just going to start with delta s.
00:49
This is going to be probably the most straightforward one to solve.
00:53
So this is the change in displacement between t equals 1 and t equals 3.
00:57
So in other words, it's s evaluated at 3 seconds minus s evaluated at 1 second.
01:06
And so all we would have to do is plug in the numbers 3 and 1 for t and see what they give us.
01:17
So first i'm going to do the s of 3 and find what that equals.
01:21
And we can just kind of plug that into a calculator and see that that's equal to 12.
01:27
And then when i plug in 1, i'm going to get a 2.
01:32
So s of 1 is 2.
01:34
So then i subtract 2.
01:36
And so delta s is going to be equal to 10.
01:43
Okay, so this is one of the answers we're looking for.
01:49
Now if we want to find the average velocity, the way to find the average velocity is just the displacement over the time...