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# 1.1 Position, Velocity, and Acceleration

Daniella Garcia-Loos

### AP Physics 1Β π‘

257Β resources
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Position, velocity, and acceleration are three fundamental concepts in physics that are related to the motion of an object. Together, these three concepts form the basis for understanding the motion of objects. In AP Physics 1, you will learn more about these concepts and how to use them to solve problems involving the motion of objects.

## Frames of Reference π¨βπ»

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 π
βΆ Motion involves the change in position of an object over a period of time, and it is measured in reference to another object.Β
 EXAMPLE:Β Two students are in a classroom sitting at their desks. Are they moving relative to each other?Β No, both students are stationary relative to each other.Are they moving relative to the solar system?Β Yes, they are on Earth and Earth is moving around the sun.Β

Essential Knowledge 3.A.1 π

An observer in a reference frame can describe the motion of an object using such quantities as position, displacement, distance, velocity, speed, and acceleration.
A frame of reference is a set of points or objects that are used as a reference for measuring positions and movements. In physics, frames of reference are used to describe the motion of objects and to assign values to physical quantities such as position, velocity, and acceleration. Here are some key points to remember about frames of reference in AP Physics 1:
• A frame of reference can be fixed, meaning it does not move, or it can be moving at a constant velocity.
• The choice of a frame of reference can affect the values of physical quantities such as position, velocity, and acceleration.
• When describing the motion of an object, it is important to specify the frame of reference in which the measurements are taken.
• In a non-accelerating frame of reference, an object's velocity is constant if and only if its acceleration is zero.
• In a frame of reference that is accelerating, an object's velocity will change even if its acceleration is zero. This is known as the "fictitious force" or the "acceleration due to the change in frame of reference."
• When describing the motion of an object in a frame of reference that is accelerating, it is useful to use the concept of relative velocity, which takes into account the acceleration of the frame of reference.

## Position π

Key Vocabulary: Position - a location relative to a fixed pointΒ
βΆ 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 velocityΒ
• 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
βΆ Still feeling a little confused on Position vs. Time Graphs? Donβt worry! Check out this video from Khan Academy for more practice!Β

### Scalar vs. Vector Quantities π«

Key Vocabulary: Scalar - quantities that are described by magnitude (a numerical value) aloneΒ
Example: She is five feet tall
• Distance and Speed are scalar quantitiesΒ
Key Vocabulary: Vector - quantities that are described by a size (magnitude) and a direction (ex. East, Up, Right, etc.)Β
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.Β
Here are some key points to remember about the difference between scalar and vector quantities in AP Physics 1:
• Scalar quantities can be added or subtracted using simple arithmetic, but vector quantities require the use of vector addition or subtraction.
• Vector quantities have a direction associated with them, while scalar quantities do not.
• Scalar quantities are described by a single number, while vector quantities are described by both a magnitude and a direction.
• Examples of scalar quantities include mass, volume, density, and temperature. Examples of vector quantities include displacement, velocity, acceleration, and force.
• Scalar quantities can be represented by a single point on a number line, while vector quantities are represented by an arrow with a magnitude and a direction.
• Scalar quantities are often denoted by lowercase letters, while vector quantities are often denoted by uppercase letters.
βΆ Are you still feeling a little confused about Scalar vs. Vector Quantities? Donβt worry! Check out this video from Khan Academy for more practice!Β

## Displacement vs. Distance π΄ββοΈ

Key Vocabulary: Displacement - how far an object is from its original positionΒ
• Vector quantity
• Express with a Sign (+ or -) or Direction (North, Down, Left, etc.)
• SI Unit: Meter (m)
• We use the symbol Ξx to indicate displacement
βΆ Typical Displacement Question: How far are you from home?Β
Key Vocabulary: Distance - how far an object has traveledΒ
• Scalar quantity
• Needs no frame of reference
• SI Unit: Meter (m)
βΆ Typical Distance Question: How far did you travel?
Displacement and distance are two important concepts in physics that are often confused with one another. Here are some key points to remember about the difference between displacement and distance in AP Physics 1:
• Displacement is a vector quantity that represents the change in the position of an object. It is defined as the final position of an object minus its initial position.
• Distance is a scalar quantity that represents the total length of the path traveled by an object. It does not take into account the direction of travel.
• Displacement has both a magnitude and a direction, while distance has only a magnitude.
• Displacement is a measure of the change in the position of an object, while distance is a measure of the total length of the path traveled by an object.
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 a total distance of 100 kilometers on a straight road. The car starts at a position of 0 kilometers and ends at a position of 100 kilometers. However, the car takes a detour halfway through its journey, traveling 50 kilometers in the opposite direction before returning to the straight road.What is the displacement of the car? In this example, the displacement of the car is 100 kilometers, since this is the change in position of the car from its initial position of 0 kilometers to its final position of 100 kilometers. The distance traveled by the car is 150 kilometers, since this is the total length of the path traveled by the car.
βΆ Still feeling a little confused about Distance vs. Displacement? Donβt worry! Check out this video from Khan Academy for more practice!Β

## Speed vs. Velocity π

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
βΆ 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 itβs above
• An object is moving towards the detector if itβs below
• The y-intercept is the initial velocity of an object
• The slope of a velocity graph is equal to the accelerationΒ
• 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
βΆ 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.Β

## Acceleration π

Key Vocabulary: Acceleration - a change in velocity (magnitude or direction)
Equation: Aavg = V/t
βΆ 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 + Β½ x 4 x 4)What is the velocity of the object from 7s - 9s?2 m/s (the area under the curve is Β½ x 2 x 2)
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