Working with the Absolute Values

Hello everyone,

My name is Ben and I'll be your scribe for today.

We started off with a very awkward question. We were asked to find the displacement of a car driving East or West from a certain place, but the question itself was unsolvable (is that a word? Anyways,). We saw that it was unsolvable because we weren't given a function or some sort of thing to represent the changes in velocity over the trip. The car could have been moving in one direction and back the same distance or it could have been moving in only one direction.

Then the next slide gave us our velocity function to find the displacement. We just used basic integration and found the displacement. Notice that we can actually find out where the object was. Normally if you were to integrate a velocity function you would only have a change in position with no exact location. We were given a reference point or a starting point so we can find out where it was after the given amount of time.

The next few slides involved the same type of work. Integrate the function to find the change in position or displacement.

Then we were asked to find the total distance of an object's travels. Note that we were supposed to find the DISTANCE. To find the distance we integrate the absolute value of the function.

The next slide was a generalization or a "What did we learn today" slide. Technically we didn't learn anything new because we already did it in chapter 6 I believe but it was a refresher.

If you integrate a velocity function you will find a change in position, it can be negative or positive or even zero depending on the direction of movement. If we were to integrate the absolute value of the velocity function we would get the total distance. If you were to take the absolute value of the integration of the velocity function you just get the change in position but it will be positive. I'm not sure if there is a use for that type of technique but I hope we talk about it tomorrow.

Homework is Chapter 18.1 Exercises 1-15 odd. The next scribe will be Paul which is not Not Paul but Francis, but by Francis I mean Not Paul.....................