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Objective: I will be able to describe position, velocity and acceleration mathematically. Bellringer. Which graph has the greater velocity? The greater acceleration?. Today:. Describing position, velocity and acceleration mathematically. Due today: Science fair Procedure and Materials.

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Bellringer

Objective: I will be able to describe position,

velocity and acceleration mathematically

Bellringer

Which graph has the greater velocity? The greater acceleration?


Today
Today:

Describing position, velocity and acceleration mathematically.

Due today: Science fair Procedure and Materials.


Velocity as slope
Velocity as Slope

How far does the baseball travel in 20 s?


Velocity as slope1
Velocity as Slope

Which has the largest velocity?


P vs t toy boat
P vs T: Toy Boat

Find velocity on each interval:



P vs t hawk
P vs. T: Hawk

Find Velocity on each interval, then sketch V vs. T



V vs t sketching
V vs. T sketching

A man fills his wheelbarrow with mulch then slowly rolls it to his garden at a constant velocity. He stops to unload the wheelbarrow, then rolls it back to the mulch pile at a constant velocity. On his way back, his wheelbarrow is much lighter so he travels twice as quickly.



V vs t sketching2
V vs. T sketching

Cordell runs from the school to Jim’s to get a hot dog. He slows down just before he gets to the road, then stops to make sure no cars are coming. He speeds back up as he crosses the road then stops at the door to Jim’s.



Bellringer1
Bellringer

Which shows an object speeding up? Slowing down?

Going at a constant, fast speed? Constant, slow speed?


Velocity is slope
Velocity is Slope…

So we can use it to write Position vs. Time in slope intercept form:

y = mx +b

d = vt + d0


Velocity is slope1
Velocity is Slope…

Graph:

y = 2x - 3

d = -2t + 1


Velocity is slope2
Velocity is Slope…

d = -2t + 1

What is the initial position of the object?

What is the velocity?


Velocity is slope3
Velocity is Slope…

Mia is 2 miles South of her house. She begins running toward her house at a velocity of 4 miles/hour.

Write an equation to represent Mia’s position.


Velocity is slope4
Velocity is Slope…

Mia is 2 miles South of her house. She begins running toward her house at a velocity of 4 miles/hour.

d = 4t - 2


Velocity is slope5
Velocity is Slope…

Breyanna races home from school to watch

her favorite cartoon. She starts out 6 km

North of her house and runs at a rate of

1 km/min. Write an equation to represent

Breyanna’s position.


Velocity is slope6
Velocity is Slope…

Jquan wants to check some books out

of the library to learn how to care for his pet

hippopotamus. He starts out 3 km East of the

library and walks 2 kilometers every 3 minutes

What is the equation for Jquan’s position?


Acceleration is slope
Acceleration is slope!

We can describe velocity using a slope intercept equation. Our variables will be v, vo, t and a. What do you think the equation will look like?



Acceleration is slope2
Acceleration is slope!

With a partner:

Write a situation with an initial velocity and an acceleration, then write an equation, then plot it on a velocity vs. time graph.


Revisiting average
Revisiting “Average”

Remember: these are averages over an interval.


Revisiting average1
Revisiting “Average”

“From 0-1 s, the average v is 1 m/s”

“From 0-1 s, the average v is 1 m/s”



Revisiting average3
Revisiting “Average”

We can treat acceleration the same way


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