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Published byChad Reeves Modified over 4 years ago

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**Graphing Motion Position vs. Time Stationary objects**

Position is same at every time (d = 0) So speed = 0 Stationary objects

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**Graphing Motion Objects with constant speed**

Position t Position changes same amount every interval If it moves 2m in 1st second, it will move 2m every second Objects with constant speed

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**Graphing Motion Objects with constant velocity**

Position t The slope is the change in position/ change in time That’s the speed or velocity! KEY FINDING: Slope of position/time graph is the speed or velocity Negative slope: object is moving in the negative direction Objects with constant velocity Change in position Change in time

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**Interpreting Graphs What’s going on here?**

Starts in a positive position Moves forward with constant speed Stops for a while Goes backward with constant speed Goes forward with constant speed to the origin (x = 0) What’s going on here? Position t

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Graphing Speed vs. Time For constant speed (could be sitting still, could be moving), speed doesn’t change Graph is just a flat line REMEMBER: This is just the slope of the position/time graph! Position Speed Case 2: Positive Constant Speed Case 2: Positive Constant Velocity Case 1: No Motion Case 1: No Motion t t

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Area under the curve Question: What does the area under the Velocity vs. Time graph tell you? 4 3 2 1 Speed (m/s) Time (s) Answer: velocity x time = distance

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**Area under the curve It works for changing velocity, too!**

4 3 2 1 Speed (m/s) Time (s) What is the total displacement? Area of the triangle: ½ * 4 * 4 = 8 meters

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**What’s happening here? We call it Acceleration**

Getting faster and faster Slope increases, therefore… Speed increases We call it Acceleration Speed t Position t

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**Acceleration Notes Acceleration is any change in speed or direction.**

Acceleration occurs when an object speeds up, slows down (or changes direction– we’ll see this later)

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Acceleration Notes Uniform (or constant) acceleration: when an object accelerates at a constant rate over a period of time. Acceleration = change in velocity/time interval Speed t

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Acceleration Notes Mathematically: a = Δv = “change in velocity” v = final velocity vo = initial velocity Units: (m/s) or m s s2 Δv = v -vo t t

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Acceleration Notes Example: A car starts out traveling at 10 m/s and accelerates to 19 m/s in a time of 3 seconds. What is the acceleration of the car? a = vf –vi = 19 m/s – 10 m/s = 3 m/s t 3s The car accelerates at 3 m/s2.

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**Finding Acceleration on a Velocity Graph**

For linear change in velocity, acceleration is the slope of the velocity graph Positive slope, so positive acceleration Speed Slope = accel = 0 Negative slope, so neg. acceleration (sometimes called “deceleration” t

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Average Speed If the speed is changing linearly (constant acceleration) Average speed is just the average of the initial and final speeds vave = v + vo t V Vave Vo

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**Average Speed: Careful!**

If I accelerate uniformly from 10 to 20 mph (miles per hour), what’s my average speed? Constant acceleration: ½ * ( ) = 15 mph If I drive 10 mph for 10 miles and 20 mph for 10 miles, what’s my average speed? 13.3 mph! Not constant acceleration, so not 15 mph!!!

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