## Velocity and other rates of change in calculus

27 Nov 2015 slides online. Rate of Change, Differential Calculus. In other words, the velocity function is the derivative of the. position function. Velocity This lesson contains the following Essential Knowledge (EK) concepts for the *AP Calculus course.Click here for an overview of all the EK's in this course. EK 2.3C1 EK 2.3D1 * AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site.® is a trademark registered and owned Calculus - 3.4 Velocity and Other Rates of Change rwalsh213. Velocity, and Rates of Change - Duration: 1:50:43. AP Calculus Section 3.4 Velocity and Other Rates - Duration: The table represents data collected in an experiment on a new type of electric engine for a small neighborhood vehicle (i.e., one that is licensed for travel on roads with speed limits of 35 mph or less).The readings represent velocity, in miles per hour, taken in 15-minute intervals on a 2 hour trip. Using derivatives to find the instantaneous rate of change (velocity) and its relationship to speed and acceleration. Determining particle motion along a line and looking at marginal cost and For free notes and practice problems, visit the Calculus course on http://www.flippedmath.com/ Lesson 3.3 Velocity and other Rates of Change AP Calculus Section 3.4 Velocity and Other Rates.

## UBC Calculus Online Course Notes For example, the velocity of a car may change from moment to moment as the driver speeds up or slows down. the derivative of some particular function everywhere, we get another function! Each one tells us about the rate of change of the previous function in this pyramid scheme.

Calculus is the study of motion and rates of change. In fact, Isaac Newton develop Calculus (yes, like all of it) just to help him work out the precise effects of gravity on the motion of the planets! In this short review article, we'll talk about the concept of average rate of change. We'll also talk about how average rates lead to instantaneous rates and derivatives. And we'll see a few Derivatives give the rates at which things change in the world. Section 3.4 Velocity and Other Rates of Change 3.4 Velocity and Other Rates of Change Instantaneous Rates of Change 127 In this section we examine some applications in which derivatives as functions are used to represent the rates at which things change in the world around us. 3.4 VELOCITY AND OTHER RATES OF CHANGE Instantaneous Rates of Change We have already seen that the instantaneous rate of change is the same as the slope of the tangent line and thus the derivative at that point. Unless we use the phrase “average rate of change”, we will assume that in calculus the phrase “rate of change” refers to the Mr. H's Calculus Page. Search this site. Navigation. Home Page. Class Announcements. Ch. 2: Limits, Continuity, Rate of Change. Functions You Should Know. Finite Limits. Infinite Limits - Vertical Asymptotes. Infinite Limits - End Behavior. Velocity and other Rates of Change. Lesson Notes: 3.4 Velocity and Other Rates of Change Calculus Example: A particle moves along the x – axis so that its position at any time t > 0 is given by the function x()tt t=−+3 12 1, where x is measured in feet and t is measured in seconds. a) Find the displacement during the first 3 seconds. b) Find the average velocity during the first 3 seconds. NOTE: This lesson has been updated to reflect the changes for Fall 2019 in the AP Calculus CED Binder. ***** Lesson Objective: ★ Estimate average and instantaneous rates of change graphically and numerically ★ Interpret distance vs. time graphs ★ Explore the concept of local linearity using graphing calculators -a rock has velocity 0 at the top so 160!32t=0 or t=5 sec-so the maximum height of a rock at t=5 sec is 160(5)!16(5) 2 =400 ft b) What is the velocity and speed of a rock when it is 256ft above the ground on the way up/down. -To find the velocity when the height is 256ft determine the two values of t which s(t) =256 s (t) =160!225 1 6t2!10+25

### AP Calculus Section 3.4 Velocity and Other Rates.

In other words an object whose velocity is v has an acceleration of which is read as "dv - dt", and is the rate of change of the velocity v, with respect to time. The big We know that a derivative is an instantaneous rate of change. for chemistry, biology, economics, geology, geography, meteorology and other sciences. To find when the particle is at rest, we take the velocity (1st derivative formula), set it AP Calculus AB : Interpretation of the derivative as a rate of change of the position function - in other words, the rate of change of the position is the velocity: . pre-calculus For a function, the instantaneous rate of change at a point is the same as the slope of the Note: Over short intervals of time, the average rate of change is approximately equal to Instantaneous velocity, mean value theorem Specifically to describe quantities and changes in quantities clearly in terms of in a familiar context of distance-time-velocity to other rate of change contexts.

### Mr. H's Calculus Page. Search this site. Navigation. Home Page. Class Announcements. Ch. 2: Limits, Continuity, Rate of Change. Functions You Should Know. Finite Limits. Infinite Limits - Vertical Asymptotes. Infinite Limits - End Behavior. Velocity and other Rates of Change. Lesson Notes:

Derivatives give the rates at which things change in the world. Section 3.4 Velocity and Other Rates of Change 3.4 Velocity and Other Rates of Change Instantaneous Rates of Change 127 In this section we examine some applications in which derivatives as functions are used to represent the rates at which things change in the world around us. 3.4 VELOCITY AND OTHER RATES OF CHANGE Instantaneous Rates of Change We have already seen that the instantaneous rate of change is the same as the slope of the tangent line and thus the derivative at that point. Unless we use the phrase “average rate of change”, we will assume that in calculus the phrase “rate of change” refers to the

## Velocity and Other Rates of Change Notesheet 03 Completed Notes Video Notes PhET Moving Man Simulation 03 N/A N/A Velocity and Other Rates of Change Homework 03 - HW Solutions Velocity and Other Rates of Change Practice 04 - HW Solutions N/A Derivatives of Trig Functions Notesheet 05 Completed Notes N/A

For free notes and practice problems, visit the Calculus course on http://www.flippedmath.com/ Lesson 3.3 Velocity and other Rates of Change AP Calculus Section 3.4 Velocity and Other Rates. Velocity and Other Rates of Change Notesheet 03 Completed Notes Video Notes PhET Moving Man Simulation 03 N/A N/A Velocity and Other Rates of Change Homework 03 - HW Solutions Velocity and Other Rates of Change Practice 04 - HW Solutions N/A Derivatives of Trig Functions Notesheet 05 Completed Notes N/A Average rate of change vs Instantaneous Rate of Change 5. How to tell if a particle is moving to the right, left, at rest, or changing direction using the velocity function v(t)

-a rock has velocity 0 at the top so 160!32t=0 or t=5 sec-so the maximum height of a rock at t=5 sec is 160(5)!16(5) 2 =400 ft b) What is the velocity and speed of a rock when it is 256ft above the ground on the way up/down. -To find the velocity when the height is 256ft determine the two values of t which s(t) =256 s (t) =160!225 1 6t2!10+25 Calculus is the study of motion and rates of change. In fact, Isaac Newton develop Calculus (yes, like all of it) just to help him work out the precise effects of gravity on the motion of the planets! In this short review article, we'll talk about the concept of average rate of change. We'll also talk about how average rates lead to instantaneous rates and derivatives. And we'll see a few