To view this presentation, you'll need to enable Flash.

Show me how

After you enable Flash, refresh this webpage and the presentation should play.

Loading...

PPT – Calculus 3.4 PowerPoint presentation | free to download - id: 77418e-ZDgwN

The Adobe Flash plugin is needed to view this content

View by Category

Presentations

Products
Sold on our sister site CrystalGraphics.com

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

3.4 Velocity, Speed, and Rates of Change

Change in position is measured in both

displacement

distance

and

The difference between the starting and ending

positions of an object

The total amount of ground covered by an object

or the total length of its path

If you were to drive 10 miles east

and then 4 miles west

10 miles east

4 miles west

Distance

Displacement

14 miles

6 miles

And the position graph would look like this

10 miles east

4 miles west

Distance

Displacement

14 miles

6 miles

Consider a graph of position (distance from a

starting point) vs. time.

Average velocity can be found by taking

The speedometer in your car does not measure

average velocity, but instantaneous velocity.

Velocity is the first derivative of position.

Mr. Murphys fall from the 196 foot platform

can be expressed with the equation

where t is in seconds and s is measured in feet.

Given the above statement, the equation for his

velocity is

which is expressed in what units?

feet/second

Find

Which is easy enough except?32 what?

t (seconds)

First, lets look at the graph of velocity. Note

that like the position graph, s(t), the y-axis

represents velocity while the x axis represents

time

v(t) (feet/second)

Since the slope of a line is based on

or in this case

we are now talking about

Acceleration

Acceleration

Is an expression of

which is a rate of change of velocity.

feet/second2

feet/second2

Example

Free Fall Equation

Wait! So what is the difference between speed

and velocity?

If the object is moving upward

or to the right

If the object is moving downward

or to the left

But speed does not indicate direction so speed

will always be positive

Wait! So what is the difference between speed

and velocity?

If an object is moving upward at a speed of 40

ft/sec

If an object is moving downward at a speed of 40

ft/sec

But regardless of the direction, the speed will

always be positive

It is important to understand the relationship

between a position graph, velocity and

acceleration

WAIT! How can you tell that acceleration is

positive?

The slope (velocity) is tilting upward so the

slope (velocity) is increasing

acc neg vel pos decreasing

acc neg vel neg decreasing

acc zero vel neg constant

acc zero vel pos constant

acc pos vel neg increasing

velocity zero

acc pos vel pos increasing

acc zero, velocity zero

Based on this graph, how can you use velocity and

acceleration to determine when an object is

speeding up or slowing down?

acc neg vel pos decreasing

acc neg vel neg decreasing

acc zero vel neg constant

acc zero vel pos constant

acc pos vel neg increasing

velocity zero

acc pos vel pos increasing

acc zero, velocity zero

time

Slowing Down

Speeding up

acc neg vel pos decreasing

acc neg vel neg decreasing

acc zero vel neg constant

acc zero vel pos constant

acc pos vel neg increasing

velocity zero

acc pos vel pos increasing

acc zero, velocity zero

time

Slowing Down

Speeding up

v and a have the same sign

v and a have opposite signs

So the moral of the story is

Rates of Change

These definitions are true for any function.

( x does not have to represent time. )

p

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Presentation Removal Request Contact Us Send Us Feedback

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Calculus 3.4" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!