1.1 Position, Velocity, and Acceleration

Frames of Reference

Essential Knowledge 3.A.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

Image courtesy of ck12.org

• 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

Scalar vs. Vector Quantities

• Distance and Speed are scalar quantities 

• Displacement, Velocity, and Acceleration are vector quantities

• 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.

Displacement vs. Distance

• 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

• Scalar quantity
• Needs no frame of reference
• SI Unit: Meter (m)

• 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.

Image Couretsy of thescienceclassroom.org

Speed vs. Velocity

• Scalar quantity
• SI Unit: Meters (m)/Seconds (s)

• Vector quantity
• SI Unit: Meters (m)/Seconds (s)

Image Courtesy of ck12.org

• 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)


Image courtesy of khanacademy.org

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)

Still Looking for more? Check out Fiveable's Live Streams on this topic:

• 🎥 Watch AP Physics 1 - Position & Velocity
• 🎥 Watch AP Physics 1 - Acceleration
• 🎥 Watch AP Physics 1 - Position vs. Time Graphs
• 🎥 Watch AP Physics 1 - Velocity vs. Time Graphs