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Describing Motion The graphs Part II…

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**The velocity in interval 3?**

The slope of a position vs time graph is? The slope of part 2? The slope of part 1? The velocity in interval 3? + 2 m/s -1m/s

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**Consider a car moving with a constant, rightward (+) velocity of +10 m/s.**

What does a velocity vs time graph look like for this motion? Zero Acceleration

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Now consider a car moving with a rightward (+), changing velocity – that is, a car that is moving rightward and speeding up or accelerating. And the graph? The car is moving in the positive direction and speeding up, it is said to have a positive acceleration.

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**The slope of a velocity time graph is …**

Slope = Δy = Change in velocity = Δx Change in time ACCELERATION The instantaneous acceleration of an object at a certain time is the slope of the velocity versus time graph at that time. It can be positive, negative, or zero.

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**Positive and negative acceleration & velocity?**

Acceleration and velocity are in opposite directions Acceleration and velocity in same direction Acceleration and velocity in same direction Acceleration and velocity are in opposite directions

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**Describe the motion of the dot.**

Constant positive velocity What does the position vs time graph look like? What does the velocity vs time graph look like? What does the acceleration vs time graph look like?

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**Describe the motion of the dot.**

A negative constant velocity What does the position vs time graph look like? What does the velocity vs time graph look like? What does the acceleration vs time graph look like?

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**Describe the motion of the dot.**

A positive velocity and a positive acceleration What does the position vs time graph look like? What does the velocity vs time graph look like? What does the acceleration vs time graph look like?

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**Describe the motion of the dot.**

A positive velocity and negative acceleration What does the position vs time graph look like? What does the velocity vs time graph look like? What does the acceleration vs time graph look like?

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**Describe the motion of the dot.**

A negative velocity and negative acceleration What does the position vs time graph look like? What does the velocity vs time graph look like? What does the acceleration vs time graph look like?

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Summary Velocity in Quad 1: positive Velocity in Quad 4: negative Acceleration: positive if slope positive negative if slope negative

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**Example: The velocity-time graph for a two-stage rocket is shown below**

Example: The velocity-time graph for a two-stage rocket is shown below. Use the graph and your understanding of slope calculations to determine the acceleration of the rocket during the listed time intervals 1 to 4 sec 4 to 9 sec 9 to 12 sec 0 to 1 sec + 40m/s2 accelerating upward +20 m/s2 Still accelerating upward -20 m/s2 Decelerating & moving upward -20 m/s2 Accelerating downward

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3,2,1,Blast off…

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Area and Graphs

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**The distance covered is the “area under” the line.**

Example 2: a) What is the acceleration in interval A? Acc = Δy = (20 – 0 m/s) = Δx (10 – 0 s) + 2 m/s2 b) What distance does it travel in first the 20s? The distance covered is the “area under” the line. Area = ½ bh Distance = ½ (20s)(40m/s) Distance = 400 m

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**e) What is the total distance?**

Example 2: c) What is the acceleration in interval B? Constant velocity of +40 m/s d) What is the distance traveled during t=20s to t = 40s? The distance covered is the “area under” the line. Area = (b)(h) Distance = (20s)(40m/s) Distance = 800m e) What is the total distance? Distance = 400m + 800m = 1200m

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Acceleration Graph m/s2 vs second

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Graph Summary

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**d vs t graph also referred to as a position time graph**

Slope of line is velocity Linear line represents a constant velocity Horizontal line represents no motion Curved line represents acceleration Steeper slope represents greater velocity Slope = Dd /Dt = velocity Distance from detector CAN be indicated

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**v vs t graph Slope of line is acceleration**

Linear line represents uniform acceleration Horizontal line represents constant velocity, a=o Curved line represents changing acceleration Steeper slope represents greater acceleration Slope = Dv /Dt = acceleration Distance from detector cannot be indicated, only direction: away is positive and towards is negative Area under curve indicates displacement

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**a vs t graph Linear line– acceleration is changing at a constant rate**

Horizontal line– uniform acceleration(the acceleration stays the same) Curved line– acceleration is changing non-uniformly Steeper slope-- greater change in a Slope = Da /Dt Area under curve indicates velocity

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**Comparing graphs No motion (v=0)**

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**Constant Velocity (a=0) positive direction**

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**Constant velocity (a=0) negative direction**

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**Describing Motion with graphs**

Classwork: Graphing Little Dudes WS # 2

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