In-Class Activities for MTH 201 Calculus Module 1A
1 like3,832 views
This document outlines the agenda for an online calculus class module on measuring velocity. The module will include a review of assignments, an activity to calculate instantaneous velocity by taking the limit of average velocity as the time interval approaches zero, a minilecture explaining this graphically, and further practice problems. Students will complete follow-up exercises on their own time and prepare for the next module.
![Summing it up
The average velocity of an object on the interval [a, b] is the
slope of the “secant line” that goes through (a, s(a)) and
(b, s(b)).](https://image.slidesharecdn.com/1a-in-200723141359/85/In-Class-Activities-for-MTH-201-Calculus-Module-1A-10-320.jpg)
![Summing it up
The average velocity of an object on the interval [a, b] is the
slope of the “secant line” that goes through (a, s(a)) and
(b, s(b)).
To find the instantaneous velocity of the object at the single
time value t = a: Move the second point b closer to a,
measure the average velocity, and repeat – look for a single
value that is being approached.](https://image.slidesharecdn.com/1a-in-200723141359/85/In-Class-Activities-for-MTH-201-Calculus-Module-1A-11-320.jpg)
![Summing it up
The average velocity of an object on the interval [a, b] is the
slope of the “secant line” that goes through (a, s(a)) and
(b, s(b)).
To find the instantaneous velocity of the object at the single
time value t = a: Move the second point b closer to a,
measure the average velocity, and repeat – look for a single
value that is being approached.
Alternate take: Think of the second point b as a + h where h
is a small distance, and let h move toward zero.](https://image.slidesharecdn.com/1a-in-200723141359/85/In-Class-Activities-for-MTH-201-Calculus-Module-1A-12-320.jpg)
![Summing it up
The average velocity of an object on the interval [a, b] is the
slope of the “secant line” that goes through (a, s(a)) and
(b, s(b)).
To find the instantaneous velocity of the object at the single
time value t = a: Move the second point b closer to a,
measure the average velocity, and repeat – look for a single
value that is being approached.
Alternate take: Think of the second point b as a + h where h
is a small distance, and let h move toward zero.
It’s also the slope of the “tangent line” that touches the
graph of s(t) at the single point (a, s(a)). If we zoomed in on
the graph of s at this point, the graph would flatten out at
appear to be equal to this line.](https://image.slidesharecdn.com/1a-in-200723141359/85/In-Class-Activities-for-MTH-201-Calculus-Module-1A-13-320.jpg)
![Summing it up
The average velocity of an object on the interval [a, b] is the
slope of the “secant line” that goes through (a, s(a)) and
(b, s(b)).
To find the instantaneous velocity of the object at the single
time value t = a: Move the second point b closer to a,
measure the average velocity, and repeat – look for a single
value that is being approached.
Alternate take: Think of the second point b as a + h where h
is a small distance, and let h move toward zero.
It’s also the slope of the “tangent line” that touches the
graph of s(t) at the single point (a, s(a)). If we zoomed in on
the graph of s at this point, the graph would flatten out at
appear to be equal to this line.](https://image.slidesharecdn.com/1a-in-200723141359/85/In-Class-Activities-for-MTH-201-Calculus-Module-1A-14-320.jpg)
In-Class Activities for MTH 201 Calculus Module 1A
- 1. MTH 201: Calculus Module 1A: How do we measure velocity? Prof. Talbert GVSU July 22, 2020
- 2. Agenda for today Review of Daily Prep assignment, and Q+A
- 3. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity
- 4. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity Minilecture: What this means from a graphical point of view
- 5. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity Minilecture: What this means from a graphical point of view Further practice with the concept
- 6. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity Minilecture: What this means from a graphical point of view Further practice with the concept For next time: Followup activities and things to do
- 7. Polling for today Go to www.mentimeter.com and enter code xx yy zz
- 8. A basic question Reminder The average velocity of a moving object is an estimate of its velocity over an interval of time. The instantaneous velocity of a moving object is its velocity at a single moment in time. Fundamental Question It’s easy to find average velocity given two points. But how do you find instantaneous velocity, where you only have one point? Activity: On your device, go to the spreadsheet set up at: https://bit.ly/201-1a
- 9. Debrief with a graph https://www.desmos.com/calculator/obpytdzxsf
- 10. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)).
- 11. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached.
- 12. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached. Alternate take: Think of the second point b as a + h where h is a small distance, and let h move toward zero.
- 13. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached. Alternate take: Think of the second point b as a + h where h is a small distance, and let h move toward zero. It’s also the slope of the “tangent line” that touches the graph of s(t) at the single point (a, s(a)). If we zoomed in on the graph of s at this point, the graph would flatten out at appear to be equal to this line.
- 14. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached. Alternate take: Think of the second point b as a + h where h is a small distance, and let h move toward zero. It’s also the slope of the “tangent line” that touches the graph of s(t) at the single point (a, s(a)). If we zoomed in on the graph of s at this point, the graph would flatten out at appear to be equal to this line.
- 15. Applying the concept Back to Mentimeter for two polling questions
- 16. NEXT TIME... Followup activities: To be done on your schedule, posted to ClassKick (watch CampusWire and Blackboard for a link). Complete by due date for 1 engagement credit. Daily Prep for Part B: Go ahead and start reading/watching video; see calendar for due date Ask questions and interact: Get on CampusWire and share thoughts, questions, and help.