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Unit 1

# 1.1 Position, Velocity, and Acceleration Peter Apps

### AP Physics 1🎡

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## Enduring Understanding 3.A 👨‍💻

All forces share certain common characteristics when considered by observers in inertial reference frames. (A frame of reference in which a body remains at rest or moves with constant linear velocity unless acted upon by forces)
Key Vocabulary: Frame of Reference - a point of view 👀
⟶ Motion involves the change in position of an object over a period of time, and it is measured in reference to another object.
 EXAMPLE: Two students are in a classroom sitting at their desks. Are they moving relative to each other? No, both students are stationary relative to each other. Are they moving relative to the solar system? Yes, they are on Earth and Earth is moving around the sun.

Essential Knowledge 3.A.1 🏘

An observer in a reference frame can describe the motion of an object using such quantities as position, displacement, distance, velocity, speed, and acceleration.

## Position 🌎

Key Vocabulary: Position - a location relative to a fixed point
⟶ You can represent position in a Position (m) vs. Time (s) Graph (pictured below) Image courtesy of ck12.org

Interpreting the Graph
• To determine which way an object is moving look at which way the Position vs. Time Graph is sloped
• A front slash / indicates that an object is moving away from the detector
• A black slash \ indicates that an object is moving towards the detector
• The slope of a Position vs. Time Graph is equal to velocity
• When the slope is a straight line it has constant velocity
• When the slope is a curved lived there is acceleration (a change in velocity)
• When the slope is zero the object is at rest
• The y-intercept is the initial displacement of an object
⟶ Still feeling a little confused on Position vs. Time Graphs? Don’t worry! Check out this video from Khan Academy for more practice!

### Scalar vs. Vector Quantities 💫

Key Vocabulary: Scalar - quantities that are described by magnitude (a numerical value) alone
Example: She is five feet tall
• Distance and Speed are scalar quantities
Key Vocabulary: Vector - quantities that are described by a size (magnitude) and a direction (ex. East, Up, Right, etc.)
Example: The gas station is five miles west from the car
• Displacement, Velocity, and Acceleration are vector quantities
Vectors can also be represented by arrows, and the length of the arrow should represent the magnitude of the described quantity. From the image below you can see the 5m arrow is smaller in length than the 50m arrow to reflect the difference in magnitude of the two quantities. ⟶ Are you still feeling a little confused about Scalar vs. Vector Quantities? Don’t worry! Check out this video from Khan Academy for more practice!

## Displacement vs. Distance 🚴‍♀️

Key Vocabulary: Displacement - how far an object is from its original position
• Vector quantity
• Express with a Sign (+ or -) or Direction (North, Down, Left, etc.)
• SI Unit: Meter (m)
• We use the symbol Δx to indicate displacement
⟶ Typical Displacement Question: How far are you from home?
Key Vocabulary: Distance - how far an object has traveled
• Scalar quantity
• Needs no frame of reference
• SI Unit: Meter (m)
⟶ Typical Distance Question: How far did you travel?
As you can see from the image below, distance takes into account the journey an object takes whereas displacement is concerned with the frame of reference of the original position. Image Couretsy of thescienceclassroom.org

 EXAMPLE:A car travels 25 meters around a circular track and ends at its original position. What is its distance?Distance → 25 Meters (The car traveled 25 Meters)What is its displacement?Displacement → 0 Meters (The car is 0 Meters from its ‘home’)
⟶ Still feeling a little confused about Distance vs. Displacement? Don’t worry! Check out this video from Khan Academy for more practice!

## Speed vs. Velocity 🏇

Key Vocabulary: Speed - describes how fast a particle is moving
• Scalar quantity
• SI Unit: Meters (m)/Seconds (s)
Equation: S = D/t
Key Vocabulary: Velocity - speed in a given direction
• Vector quantity
• SI Unit: Meters (m)/Seconds (s)
Equation: V = x/t
⟶ You can represent velocity in a Velocity (m/s) vs. Time (s) Graph (pictured below) Image Courtesy of ck12.org

Interpreting the Graph
• To determine which way the object is moving look at whether the Velocity vs. Time Graph is above or below the horizontal axis (x-axis)
• An object is moving away from the detector if it’s above
• An object is moving towards the detector if it’s below
• The y-intercept is the initial velocity of an object
• The slope of a velocity graph is equal to the acceleration
• When the slope is zero the object has constant velocity
• When the slope is a straight line it has constant acceleration
• When the slope is a curved line there is changing acceleration
• The area under the curve is displacement
• The object is stopped when y = 0
⟶ The table below is a type of motion cheat sheet. Memorizing this will help you ace any quizzes or tests with graph interpretation present!
 Velocity Acceleration Type of Motion V = 0 A = 0 At rest V = (+) or (-) A = 0 Constant velocity V = (+) A = (+) Speeding up V = (-) A = (-) Speeding up V = (+) A = (-) Slowing down V = (-) A = (+) Slowing down
 FRQ PRACTICE:Want more practice with Velocity and Average Velocity? Check out these FRQs from the 2016 AP Physics 1 exam.

## Acceleration 🚀

Key Vocabulary: Acceleration - a change in velocity (magnitude or direction)
Equation: Aavg = V/t
⟶ You can represent acceleration in an Acceleration (m/s/s) vs. Time (s) Graph (pictured below) Interpreting the Graph
• The y-intercept is the initial acceleration of an object
• When the slope is zero the object has constant acceleration
• The area under the curve is velocity
 EXAMPLE:(Reference the Graph above to answer the following questions)What is the velocity of the object from 0s - 7s?20 m/s (the area under the curve is 4 x 3 + ½ x 4 x 4)What is the velocity of the object from 7s - 9s?2 m/s (the area under the curve is ½ x 2 x 2)
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