Reimann Sums- Cooper Krause Jan 29th

Cooper Krause
January 29th, 2013

We started class with a quiz that we will be getting back and possibly super correcting today. Then... the learning began.

We started by referring back to the question Mr. OB asked us last class.

True or False: An object that has a negative acceleration is slowing down.
If I remember correctly, 7 of us answered the correct answer of true, and 4 answered the incorrect answer of false. A ratio of slightly above 50% of the class got the question correct. Decent job guys, decent job.

The answer is false because: when an object has a negative acceleration, it means the velocity is decreasing. If the velocity is positive and decreasing, then the speed is decreasing. However, if the object has a negative velocity and a negative acceleration than the speed is actually increasing in the negative direction. The key to what we have been talking about the last few days is that speed does not take direction, whether it be positive or negative, into account. In other words that have been repeated many times recently, speed is the absolute value of velocity.

To solidify the ideas of speed, velocity and acceleration and how they are related we went over IW #5 which asked generalized questions about the topics.
Things to Remember:
-When the speed is increasing the velocity and acceleration have the same signs.
-When the speed is decreasing, the velocity and acceleration have opposite signs.
-Acceleration is the derivative of velocity
-Velocity is the derivative of position

Next we started  PART 2 OF CALCULUS with Reimann Sums.


We started by using the concept velocity X time = distance to complete the Reimann sum worksheet. We found that Reimann sums are used to estimate the max and min distance traveled when we know know certain speeds at certain times.




To reach our minimum value for example we assumed that the velocity remained at 30 ft/sec for the first 2 seconds and then at t=2 instantaneously switched to the new assigned value. For the maximum value we assumed that the velocity instantaneously went to 36 after t=0 and so on. We found that if we double the amount of segments where a velocity is assigned, so every one second instead of 2, no matter what we assigned for the new velocity values the error between the max and min sums was always the same. The error was also half of the original error when we doubled the amount of segments.

This picture as a graphical analysis of an upper and lower Reimann Sum. The upper Reimann sum includes the blue rectangle at the top as well as the red which is representative of the lower Reimann sum. The blue box itself represents the error between the two Reimann sums.
This final picture shows a plausible function connecting the original velocity/time coordinates assigned: A, B, C, D, E and F. This plausible function sets down an amount of segments that approaches infinity. There is no difference between the max and min Reimann sums. This area is known as the definite integral.

That's pretty much where we ended guys. Have fun with IW #6 and super corrections. I know you willll!!!!!!!!