## October 03, 2006

### Scribe Post

It's Mark again, and this time it's the real deal...

Question ONE
Charlotte drove to Gimli over the weekend. The Graph shows her distance travelled over time.

NOTE: people may have differences in solutions, relating to what points they chose.

A) What was her average speed:
i)Over entire trip? What kind of driver is she?
Avg speed=40km/h for the entire trip

to solve for the average speed, take two points and find the difference between the two points. Divide the difference in distance by the difference in time. This is also known as:

Rate of change, delta y/ delta x, slope

ii) Over the first hour?
45km/1hr= 45km/hr during the first hour

iii) last hour?
(100km-45km)/1hr= 55 km/hr during the las hour

iv) First half hour?
38km/0.5hr= 70km/hr during first half hour

v)over last half hour?
(100km-50km)/0.5hr=100km/hr
B) What happened at the one hour mark? How long did it last?
At the one hour mark, Charlotte stopped driving. You could ttell she stopped because she was not gaining or losing distance starting at that time. She stopped for about thirty minutes

What would happen... ?
If we found Charlotte's speed the first quarter of an hour ?

20km/0.25hr=80km/hr

If we found Charlotte's speed the first eighth of an hour (7min!!!)?

15km/0.125hr=120km/hr

If we continue to narrow down a specific time, the secant line begins to transform into the tangent line. The tangent line finds the velocity of one time period.

Vocabulary

SECANT- A line that cuts a graph in 2 or more places. Finding the slope of the secant line gives us the velocity for a time interval (distance vs. time graphs). Secants can be applied to any graph, we just use "distance vs. time" because it is easy to understand.

TANGENT- A line that touches one point on a graph. The slope of the tangent line determines the instantaneous value for one plave in time (i.e. velocity at 20 seconds).

CONCAVITY- The "bendyness of a graph". if the curve of a graph opens down, we call the curve concave down. if the curve of a graph opens up, we call the curve concave up.

DERIVATIVE- The instantaneous point on a tangent line, rate of change at one point in time.

Not included in this SP, is the symbolic method of solving a graph.

HW: section 2.1 odds, 6 and 12

Same Sp for tomoorow as i posted on the test Sp

You are probably wondering why i chose such a large font. I chose this font size because it makes you want to read the text. The letters are not so tiny. I have noticed that if a Scribe post looks really long i don't feel like reading it all. Now you can scan easily for BIG key words.=)

christian said...

Does anyone here feel unworthy to be in the same class as Mark, or is it just me?? MAN what a post. On with my comment..

It was mentioned:

"If we continue to narrow down a specific time, the secant line begins to transform into the tangent line."

Perhaps secant lines just act like tangent lines, instead of 'transforming'?. I don't know.. people comment please?

Manny said...

I think they're different Christian.

Secant lines hit the graph in two or more places, and tangent lines hit the graph in only one place.

And so as the secant line gets closer and closer and closer, it eventually hits one spot, but really they're is a tiny tiny value that it hits in both places, but the distance between the two is so insignificant we don't count it. That's what I'm guessing on.

Lani said...

Hi Mark,

I like your strategy; it works! And your explaining it for everyone at the end is valuable too!

Very nice job!

Best,
Lani