2.3-2.4

Motion!!!

Now we're moving

Derivation:

good, bad, ugly

What does it mean to derive something?

The good:

This is how we learn.

start at something we know,

add something else, modify

get somewhere new!!

The bad:

It's MATH

The ugly:

Not always intuitive.

Can get hairy.

Example what can we do with this? (acceleration)

Start with the 1's and 2's what do they mean?

Let us change them, but to what?

What would be a good change for the 1's? Why?

Now this equation takes the form of:

Constant Acceleration:

any examples?

All of what we will do with motion

will have constant acceleration

(rare exceptions will be stated)

From the definition of acceleration

we have DERIVED an equation for Velocity.

Yeah, but I thought we alread had an equation for velocity?

So what is the difference between them

and when would you use them?

Following the same flavor with acceleration, we can change velocity to:

What can we do with this average velocity?

What is an average?

what is the average of 2 numbers?

say 0 and 10?

We can do the same for the average of two velocities.

****Caution when does this not work?****

We are ok as long as we have a constant acceleration.

Now what, what's going on, why are we doing this?

Deriving quantities from other base quantities is all

about relationships. We need to take thing we know

and express new concepts in terms of those known ones.

The math can get messy, but we are still ok here.

Recall we had an equation for x but there was an average

velocity in it, and we found a different equation with

average velocity.

Did we do it, is this right?

Can we do anything else?

Yup, one more substitution.

one more!!!!!

Collect the three:

To use these equations I need:

A. Initial position

B. Initial velocity

C. Acceleration

D. Time

E. Some / All : Depends

To solve for 2 (final position) directly

I only need:

1. initial position 2. final position

3. inital velocity 4. final velocity

5. acceleration 6. time

A. 1, 3, & 5

B. 1, 3, & 4

C. 1, 3, 4, & 5

1

2

3

To solve for final position

without time (assuming you

have the other variables):

A. Equation 1

B. Equation 2

C. Equation 3

To solve for final Velocity without distance (assuming you have other variables):

A. Equation 1

B. Equation 2

C. Equation 3

What is the overall assumption

about Acceleration in all of these?

A. it is averaged

B. it is zero

C. it is constant

Here is an example straight from the text:

How long does it take a car to cross a 30.0 m intersection

after the light turns green if the car accelerates from rest at a constant 2.00 m/s^2?a

what values are defined here?

(what are we looking for)

What basic equations have these variables?

Solve, number, units, ballpark

x = 30.0 m

a = 2.00 m/s^2

t = ?

x = 30.0 m

a = 2.00 m/s^2

t = ?

Technically and specifically we

don't have inital position or velocity

rest = initial velocity = zero

cross = start at one end finish other

initial position = zero

**A car slows down uniformly**

from a speed of 21.0 m/s to

rest in 6.00 s. How far did it

travel in that time?

from a speed of 21.0 m/s to

rest in 6.00 s. How far did it

travel in that time?

**what is defined?**

A. 1, 2, 3

B. 2, 4, 6

C. 1, 3, 5

D. 1, 2, 4

E. 2, 3, 4

A. 1, 2, 3

B. 2, 4, 6

C. 1, 3, 5

D. 1, 2, 4

E. 2, 3, 4

**Can we solve this with**

just one equation?

A. YES B. NO

1

2

3

just one equation?

A. YES B. NO

1

2

3

**what are we looking for?**

A. 1 B. 3 C. 5

A. 1 B. 3 C. 5

**So we have:**

x = 30.0 m

a = 2.00 m/s^2

t = ?

tips:

Draw, define, describe

Basic equations

Solve, numbers, units,ballpark

3D be SNUB

Define: list what you know, or is

defined in the problem.

Also list what you don't.

"Where in reality would you be able to find something with constant velocity and acceleration?"

"Can you explain displacement or area under a curve and why it is important."

"Are there other graphs like the position vs. time or acceleration vs. time graph where the area under the curve gives us new information?"

"How do you know what set of kinematic equations are we supposed to use for a given problem?"

"What would be the integral of an acceleration vs. time graph?"

"Can you explain finding position from velocity equations?"