Motion 🚗

A Descriptive Model for Particles

Regents Physics 2024-25 with Mr. Porter

Contents

Toy Buggy Observations 🚗

In your lab notebook write down 2 of the following...

  • 👀 what do you see? (observations)
  • 🤔 what do you think? (hypotheses)
  • 💭 what do you wonder? (what questions could you ask to support hypotheses)

Buggy Lab 🚗

Objective:

  • Determine if your toy buggy moves in a consistent manner by developing a relationship between position and time.

Notes

  • Use time as your independent variable
  • Your Lab Setup is based on an assigned initial set up

Buggy Lab 🚗

Objective:

  • Determine if your toy buggy moves in a consistent manner by developing a relationship between position and time.

Notes

  • Use time as your independent variable
  • Your Lab Setup is based on an assigned initial set up

Lab Results:

  • The buggies moved with a constant velocity
    • means that it changed its position equal amounts for each equal change in time
  • Velocity () is represented by the slope of the position vs. time graph
    • how "fast"
    • AND what direction
  • Speed is the steepness of the slope:
    • it tells us the rate that position changes with time
    • steeper slope == faster
  • The initial position ( or ) of the object is the vertical intercept
    • it tells us where the object is at clock reading 0.

Mathematical Models

General Mathematical Mode:

Specific Mathematical Model (example):

Narrative Model:

"The toy car started at a position of 250 cm and moved in the positive direction at a speed of 25 cm/s."

Defining "How Far"

Who went further? Dorothy or Toto?

Make an arguement for both cases

Vector vs. Scalar

Vector

  • Physical Quantity that describes magnitude (size) and direction
  • indicated with an ➡️ above the symbol
    • i.e. or or

Scalar

  • Physical quantity that describes the magnitude (size) of something

Displacement

  • Change in position of an object
  • Includes direction (vector quantity)

Distance

  • the magnitude (or size) of displacement between two positions (scalar quantity)
  • more often referred to as distance traveled which is the total length of the path traveled between two positions

Position

  • Where an object is at any particular time in coordinate system (vector)
  • "Location"

Speed vs. Velocity:

  • Velocity is a vector quantity
    • how fast and what direction
  • Speed is a scalar quantity
    • how fast

Describing Motion

Each description should include:

  • Starting position
  • Direction of motion (positive direction, no motion, or negative direction)
  • Type of motion (at rest, constant velocity, speeding up, slowing down or some combination of these)
  • Relative speed (slow, medium, fast, slower, faster—this is only meaningful with there is more than one part of the motion or when you are comparing two or more objects)

Lets Practice

Describe the motion of each graph

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Lets Practice

Describe the motion of each graph

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Lets Practice

Describe the motion of each graph

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Lets Practice

Describe the motion of each graph

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Lets Practice

Describe the motion of each graph

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Lets Practice

Describe the motion of each graph

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Motion Maps

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Motion Maps


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Motion Maps Notes

  • Each dot represents one unit of time
  • The numberline is the position of the object
  • The separation of the dots and length of the arrow represents the velocity of the object
  • Stacked dots represent an object that is motionless

Motion Map Practice

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Motion Map Practice

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Motion Map Practice

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Motion Map Practice

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Motion Map Practice

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Practice: Complete individually and compare

Given the following position vs. time graph

  1. Draw a motion map with one dot for each second
  2. Describe the motion in words

More Practice

Given the following motion map, where positions have been recorded with one dot each second,

  1. Draw a position vs. time graph
  2. Describe the motion of the object in words

Motion Sensor Lab

Analyzing Position-Time (XT) Graphs

For the following position vs. time graph, consider the positive direction to be north.

  1. When is the object moving North? South?
  2. When is the object stopped?
  3. When is the object North of the origin?
  4. What is the velocity of the object at s? s? s? When it is at the origin?

Average vs. Instantaneous

  • Average - what is something over a period of time,
  • Instantaneous - what is something at that exact moment in time,

Velocity vs. Speed

Velocity

Speed

Instantaneous Values:

  • "at that moment"
  • Value at a specific time

Instantaneous Velocity

  • Velocity at a specific time
  • The slope of the position vs. time graph at that time measurement

Instantaneous Speed

  • Magnitude of the velocity

Visualizing Instantaneous Velocity

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Visualizing Instantaneous Velocity

Analyzing Position-Time (XT) Graphs

  1. When does the object change directions?
  2. What is the total distance the object travels?
  3. What is the total displacement of the object?
  4. What is the average velocity of the object?
  5. What is the average speed of the object?

Average Velocity

Dispalcement divided by the change in time.

"The average slope of the graph"

Average Speed

Total distance divided by change in time

Analyzing Position-Time (XT) Graphs

For the following position vs. time graph, consider the positive direction to be north.

  1. When is the object moving North? South?
  2. When is the object stopped?
  3. When is the object North of the origin?
  4. What is the velocity of the object at s? s? s? When it is at the origin?

Analyzing Position-Time (XT) Graphs

  1. When does the object change directions?
  2. What is the total distance the object travels?
  3. What is the total displacement of the object?
  4. What is the average velocity of the object?
  5. What is the average speed of the object?

Average Velocity

Dispalcement divided by the change in time.

"The average slope of the graph"

Average Speed

Total distance divided by change in time

Instantaneous Values:

  • "at that moment"
  • Value at a specific time

Instantaneous Velocity

  • Velocity at a specific time
  • The slope of the position vs. time graph at that time measurement

Instantaneous Speed

  • Magnitude of the velocity

Velocity vs. Time Graphs

VT Graphs

  1. Draw the velocity vs. time graph for an object whose motion produced the position vs. time graphs shown below.
  2. For many graphs, both the slope and area between the line and the horizontal axis have physical meanings. What does the slope of the position vs. time graph tell you about the motion of an object?

VT Graphs

  1. Complete the following chart and show your work
from XT Graph Area "under the curve" of VT Graph
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2
3

VT Graphs

  1. Looking at the velocity vs. time graphs, determine the units for a square of area on the graph.
  2. What does the "area under the velocity-time graph" tell you about the motion of the object?

Area of VT Graph

  • Area "under the curve" represents the displacement (change in position) of the object.
  • Areas can be negative because that represents the direction

  • Add multiple segments together, including the sign to get the total displacement of a piecewise motion

Area of VT Graph

  1. Area = = m
  2. Area = = m
  3. Area = = m

Up Next...

Changing Velocities...

Defintions & Notes

  • Displacement indicates how far an object ends up from its initial position, regardless of its total distance traveled.
  • Average velocity is displacement divided by the time interval over which that displacement occurred. Slope of position time graph over a time duration.
  • Instantaneous velocity is how fast an object is moving at a specific moment in time. Slope of position time graph at a specific time.
  • Acceleration tells how much an object’s speed changes in one second.
    • When an object speeds up, its acceleration is in the direction of motion.
    • When an object slows down, its acceleration is opposite the direction of motion.

Thinking about graphical relationships

Position-time graphs

  • To determine how far from the detector an object is located, look at the vertical axis of the position-time graph.
  • To determine how fast an object is moving, look at the steepness (i.e. the slope) of the position-time graph.
  • To determine which way the object is moving, look at which way the position-time graph is sloped.
  • A position-time slope like a front slash ↗️ / means the object is moving away from the detector.
  • A position-time slope like a back slash ↘️ \ means the object is moving toward the detector
  • Instantaneous velocity is found by taking the slope of the tangent line to a position-time graph
.

Velocity-time graphs

  • To determine how fast an object is moving, look at the vertical axis of the velocity-time graph.
  • To determine which way the object is moving, look at whether the velocity-time graph is above or below the horizontal axis.
  • An object is moving away from the detector if the velocity-time graph is above the horizontal axis.
  • An object is moving toward the detector if the velocity-time graph is below the horizontal axis.
  • To determine how far an object travels, determine the area between the velocity-time graph and the horizontal axis.
  • On a velocity-time graph it is not possible to determine how far from the detector the object is located.
  • Most everyday motion can be represented with straight segments on a velocity-time graph.
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Acceleration

  • Negative Acceleration does not always mean slowing down
  • Negative Acceleration means the velocity is changing in the negative direction

Acceleration: Increasing vs. Decreasing Speed

  • Speeding Up: Acceleration and velocity have the same sign
  • Slowing Down: Acceleration and Velocity have opposite signs

Shapes of VT Graphs

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Shapes of VT Graphs

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Shapes of VT Graphs

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Shapes of Graphs

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Shapes of Graphs

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Shapes of Graphs - Summary

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.
fit,

Graph That Motion

https://www.physicsclassroom.com/Physics-Interactives/1-D-Kinematics/Graph-That-Motion/Graph-That-Motion-Interactive

Reminders

To determine how far (displacement) an object travels, determine the area between the velocity-time graph and the horizontal axis.

The slope of the Velocity vs. Time Graph is Acceleration

VT Graphs

For each object...

  1. Determine the displacement between and seconds.
  2. Determine the average acceleration during the first sec.
  3. Describe the motion in words.
  4. Draw the position vs. time graph that goes with the VT Graph.
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VT Graph 2

  1. Give a written description of the motion.
  2. Determine the displacement of the object from to seconds.
  3. Determine the displacement of the object from to seconds.
  4. Determine the displacement of the object from to seconds.
  5. Determine the object’s acceleration at t = 4 seconds.

Kinematic Equations...from Regents Reference Table

Definitions:

Average Speed/Velocity:

Acceleration:

Equation of line for VT Graph (no displacement):

Quadratic Position Equation (no final v):

Time independent equation (no t):

  • → average speed or velocity
  • → distance or displacement
  • → time
  • → acceleration
  • → change in velocity
  • → initial velocity
  • → final velocity

Note

They are the same!

You should use to be consistent with Regents Reference Table

Kinematic Cross Diagram for Problem Solving

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Kinematic Cross Diagram

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Identifying Equations

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Non-reference Table Equations

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Using the Cross Diagram

  1. Setup
    1. Write down the cross
    2. Write down the known variables and underline those variables in the cross
    3. Star (or circle) the variable that is unknown and is being solved for
  2. Planning
    1. Circle the variables that are involved in this problem
    2. Use the equation that involves those four variables
  3. Execution
    1. Solve the problem
    2. You can circle twice: solve for first unknown to use in second equation

Example

A poorly tuned car accelerates from rest to a speed of 28 m/s in 20 seconds. What is the acceleration of the car? How far does the car travel in this time?

Practice

A speedboat increases its speed from 14.3 m/s to 31.1 m/s in a distance of 274 m. Determine the time over which this acceleration occurs.

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Complete on a whiteboard with a partner from your lab table

Physics is more than plugging numbers into equations!

Solve 🧩🤔➡️🔍

A poorly tuned car accelerates from rest to a speed of 28 m/s in 20 seconds. What is the acceleration of the car? How far does the car travel in this time?

🚨 Remember to:

  1. Sketch and Translate
  2. Simplify and Diagram
  3. Represent Mathematically
  4. Solve + Evaluate

🔎 Hint:

Use a graph or graphs to solve the problem.

Multiple Representations:

  • Verbal: Describes the motion of the car in a narrative manner.
  • Pictorial: A picture shows the initial and final motion of the car.
  • Diagrammatic: The picture is simplified and shows the motion of the car over multiple clock readings.
  • Graphical: Three representations that show how the position, velocity, and acceleration of the car vary over time.
  • Mathematical: Describes the velocity of the car as a function of time and the position of the car as a function of time.

Problem Solving Process:

  1. Sketch and Translate
  2. Simplify and Diagram
  3. Represent Mathematically
  4. Solve + Evaluate

1. Sketch

  • A sketch of the object or objects at the beginning of the motion, at the end of the motion, and any important points in between where the motion changes (i.e. if the acceleration of the object changes).
  • A coordinate system Label the axes and the origin (position 0).
  • Symbols that represent the time, position, and velocity of each object at each moment you have draw above. Use subscripts to depict different times and different objects (i.e. or or ). This step defines the symbols that you will use later in calculations.
  • Draw arrows to show the acceleration and velocity of the object between each position (or write or )

1. Translate

Now that you have a sketch of the situation you should organize everything you know and want to find. Therefore you should:

  • Make a table listing all of the symbol values that are known for the problem or that can be determine from simple geometry. Check that the signs are consistent with your sketch and its coordinate system. Also list known relationships, such as , even if you don't know the values yet. At this point do any unit conversions that are necessary.
  • Make a list of the unknown quantity or quantities you'll need to answer the question.

2. Simplify and Diagram (Physics Diagrams)

  • From our sketch we will no create physics diagrams...for motion this includes:
    • position vs. time graph
    • velocity vs. time graph (most useful)
    • acceleration vs. time graph

3. Represent Mathematically

  • mathematical description of the process
  • turn physics diagrams into equations:
    • use area of v-t to calc displacement
    • use slopes to calculate velos, or accelerations
    • use position functions to find final positions

4. Solve + Evaluate

  • substitute in given quantities and solve!
  • Evaluate: does this number make sense? Is it a reasonable solution?

Example:

A poorly tuned car accelerates from rest to a speed of 28 m/s in 20 seconds. What is the acceleration of the car? How far does the car travel in this time?

Sketch and Translate

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Simplify and Diagram

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Represent ➡️ Solve:

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