Using Graphs and Equations to Describe Motion

Using Graphs and Equations to Describe Motion

Position-Time Graphs,

Velocity-Time Graphs

Position-Time Graphs,

Velocity-Time Graphs

How can we calculate velocity?How can we calculate velocity?

Equation: Equation:

€

v =d

t

Units:

€

m

s

How can we use position-time graphs to describe motion?

How can we use position-time graphs to describe motion?

5

4

3

2

1

0

Position (m)

0 5 10 15 20 25Time (s)

Summary: Position-time graphsSummary: Position-time graphs

Position - read y value at time t Displacement - subtract positions Distance - add legs Velocity - slope

Position - read y value at time t Displacement - subtract positions Distance - add legs Velocity - slope

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ΔyΔx

=y2 − y1

x2 − x1

How can we use velocity-time graphs to describe motion?

How can we use velocity-time graphs to describe motion?

50

40

30

20

10

0

Velocity (m/s)

0 5 10 15 20 25Time (s)

Summary: Velocity-time graphsSummary: Velocity-time graphs

Instantaneous velocity - read y value at time t Average velocity - add velocities and divide by 2 Distance/Displacement - area under the line Acceleration - slope

Instantaneous velocity - read y value at time t Average velocity - add velocities and divide by 2 Distance/Displacement - area under the line Acceleration - slope

€

ΔyΔx

=y2 − y1

x2 − x1

Formulas for Accelerating Objects:

Formulas for Accelerating Objects:

Finding average velocity (two formulas): Finding average velocity (two formulas):

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v =d

t(already know this one)

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v =v f + v i

2

(we know this one, too, but it is not in the reference table!)

Formulas for Accelerating Objects:

Formulas for Accelerating Objects:

Finding acceleration: Finding acceleration:

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a =Δv

t=v f − v it

Formulas for Accelerating Objects:

Formulas for Accelerating Objects:

Finding final velocity given constant acceleration:

Finding final velocity given constant acceleration:

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v f = v i + at

Wow! Looks like y = mx + b

Formulas for Accelerating Objects:

Formulas for Accelerating Objects:

Finding displacement of an acceleration object: (two formulas):

Finding displacement of an acceleration object: (two formulas):

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d = v it +1

2at 2 What does this look like

on a graph?

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v f2 = v i

2 + 2ad

Free FallFree Fall

Is gravity the same everywhere? NO Shape of the Earth - oblate spheroid Sketch: Gravity smaller at higher altitudes and at

equator (greater distance to the center of the Earth)

Is gravity the same everywhere? NO Shape of the Earth - oblate spheroid Sketch: Gravity smaller at higher altitudes and at

equator (greater distance to the center of the Earth)

How does velocity change as a ball is thrown in the air and

allowed to fall?

How does velocity change as a ball is thrown in the air and

allowed to fall? Graphs: Graphs:

Example:Example:

A ball is thrown in the air. As it leaves your hand, it is traveling upward at 20 m/s.

Describe how the velocity changes as the ball rises and falls:

A ball is thrown in the air. As it leaves your hand, it is traveling upward at 20 m/s.

Describe how the velocity changes as the ball rises and falls:

At what time will the velocity be 0 m/s? At what time will the velocity be 0 m/s?

How high does the ball go? How high does the ball go?

What is the displacement of the ball? What is the displacement of the ball?