What a minute...

Today in class we were looking at the graphs of average speeds, which we called "secant lines". We agreed that to calculate the average speed, we would take the change in distance and divide it be the change in time. So we used this formula and found that our average speeds were

• 8 m/s from 0 secs to 50 secs
• 10.5 m/s from 25 secs to 50 secs
• 12 m/s from 40 secs to 50 secs

We noticed that as the average speeds increased, the slopes of the associated secant lines also increased (they got steeper).

Then we talked about finding the instantaneous speed at 50 secs. Students started mentioning strategies that sound very much like the strategy for finding average speed. They said we needed to use 2 points, and to use the average speed formula above.....

How is their strategy finding instantaneous speed? How is it any different than finding average speed? If their strategy is different, what makes it different?

We finished the class by using our calculators to zoom in on two points really close to the point, (50,400), in order to calculate the slope. Why should we care about the slope of these two points?