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Unit 1: Motion in One Dimension

Motion …

Kinematics in One Dimension

The source of content for this course is www.physicsclassroom.com

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Unit Objectives/LessonsStudents will be able to…1. One Dimensional (1-D) Kinematic quantities and

relationships; solve basic 1-D motion problems• Displacement and Velocity quantities and relationships• Acceleration quantities and relationships

2. 1-D Motion by Graphical Means using linear motion graphs: displacement (d) vs. time (t) and velocity (v) vs. time (t)

3. Free Falling body kinematics using primary kinematic equations

4. 1-D Motion by Algebraic Means using primary kinematic equations

Unit 1: Motion in One Dimension

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Kinematics

Science of describing the motion of objects using words, diagrams, numbers, graphs, and equations

Unit 1: Motion in One Dimension

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Lesson Objectives

Students will be able to…• Understand the 1-D Kinematic concepts of

displacement, time, velocity and acceleration• Understand scalars and vectors as

measurement quantities• Solve basic 1-D motion equations

Lesson 1: 1-D Kinematics Intro

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Scalar vs. Vector – measurement quantities

scalar: have magnitude (value), but no direction.Examples: time, mass, distance.Mass has a number value (like 58 kg), but we don't give it a direction (like “East”).

vector: have magnitude and directionExamples: velocity, force, displacement.Force has a magnitude (like 37 N) and a direction (like "pushed to the left").

Lesson 1: 1-D Kinematics Intro

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Displacement and Time

Essential information needed to describe the motion of an object

Displacement of an object is always measured from some reference point

- usually “zero” as the motion’s starting point

Lesson 1: 1-D Kinematics Intro

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Displacement vs. Distance

Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.

Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's overall change in position.

Lesson 1: 1-D Kinematics Intro

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Displacement vs. Distance

Distance ?Displacement ?

Lesson 1: 1-D Kinematics Intro

A

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Displacement vs. Distance

Example 1

Lesson 1: 1-D Kinematics Intro

Set Up Table – Time, Distance & Displacement

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Displacement vs. Distance

Simple formula for calculating the displacement of an object is…

Δd = df - di

• Δ symbol is the Greek letter “delta” and means “a change in…”• Subscript “f” and “i” stand for final and initial

Lesson 1: 1-D Kinematics Intro

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Displacement vs. Distance

Example 2: A truck going east passes a mark on the road that says 150m, and then passes another one 10s later that says 450m. Determine the truck’s displacement during the 10s period.

Δd = df - di =

Lesson 1: 1-D Kinematics Intro

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Displacement vs. DistanceExample 3: You start walking home from school. After walking 1.5 km East, you get a phone call from your mom asking if you can meet her at the mall. You will have to turn around and walk 2.3 km West. Determine your distance and displacement to get to the mall.

Distance =

Displacement =

Lesson 1: 1-D Kinematics Intro

Do Worksheet Problems – Distance & Displacement

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Velocity vs. Speed

Speed is a scalar and refers to “how fast an object is moving”. e.g. “we drove at 65 km/hr.”

Velocity is a vector and refers to "the rate at which an object changes its position.”e.g. “we drove at 65 km/hr east.”

Lesson 1: 1-D Kinematics Intro

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Average VelocityThis leads to the first major formula, the calculation of average velocity:

vavg = average velocity (m/s)Δd = df - di = displacement (m)Δt = tf - ti = time (s)

Why is this considered the “average” velocity?

Lesson 1: 1-D Kinematics Intro

t

dvavg

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Average Velocity

Example 4: I try to run the 100m race to break the world's record. Unfortunately, it takes me 16.83s to complete the run. Determine my average velocity.

This is my average velocity. What was my speed?Was is constant for 100m?

Lesson 1: 1-D Kinematics Intro

t

dvavg

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Average Velocity

Example 5

Lesson 1: 1-D Kinematics Intro

Set Up Table – Time, Speed & Velocity

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Average Velocity

Note that in the example, the displacement and the velocity were positive numbers.

• Positive and negative tell you direction with respect to the reference point (these are vectors!)

• Positive velocity means you are moving forward, to the right, or up, while negative means you are going backwards, to the left, or down

Lesson 1: 1-D Kinematics Intro

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Average Velocity

Example 6: Look back at Example 3. Determine your speed and velocity if the walk took you one hour and ten minutes. Use standard units and the correct sig digs.

speed =

velocity =

Lesson 1: 1-D Kinematics Intro

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Uniform Motion

Lesson 1: 1-D Kinematics Intro

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Uniform Motion

Assume object is moving at the same velocity the whole time.• If velocity is always the same, it has a constant

velocity - the object is not accelerating• Also call this uniform motion• Uniform motion is the easiest kind of motion to

describe and measure

Lesson 1: 1-D Kinematics Intro

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Instantaneous Velocity

In real life we often have to deal with an object traveling without uniform velocity.

An example is driving with a friend in a car.

Instantaneous velocity is the velocity of an object at one moment of time

Lesson 1: 1-D Kinematics Intro

Do Worksheet Problems – Speed & Velocity

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Acceleration

Lesson 1: 1-D Kinematics Intro

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Acceleration

Acceleration:- describes the change in velocity over time- it is a vector – magnitude and direction.

In real life we typically deal with an object traveling without uniform velocity.

An example is driving with a friend in a car.

Lesson 1: 1-D Kinematics Intro

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Acceleration

Lesson 1: 1-D Kinematics Intro

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Average AccelerationThis leads to the second major formula, the calculation of average acceleration:

aavg = average acceleration (m/s2)Δv = vf - vi = velocity (m/s)Δt = tf - ti = time (s)

Why is this considered the “average” acceleration?

Lesson 1: 1-D Kinematics Intro

t

va avg

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Average Acceleration

Example 6: A car moving at 50km/h accelerates to 60km/h in 7.0 seconds. Determine its acceleration.

Lesson 1: 1-D Kinematics Intro

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Negative Acceleration

In physics, acceleration is not always an increase in velocity. It can also be a decrease in velocity.

• Since acceleration is a vector, it has direction

• We call a decrease in velocity of an object traveling forward a negative acceleration

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Negative Acceleration

The general RULE OF THUMB is:

If an object is slowing down, then its acceleration is in the opposite direction of its motion.

Lesson 1: 1-D Kinematics Intro

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Negative Acceleration

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Negative Acceleration

Lesson 1: 1-D Kinematics Intro

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Negative Acceleration

Example 7: You are walking down the street when you see an enormous, 112kg pickle rolling towards you at 12 m/s. Surprised, you jump in front of it and begin pushing on it until you finally bring it to a stop 17.5s later. Determine the acceleration of the pickle.

Lesson 1: 1-D Kinematics Intro

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Instantaneous Acceleration

In real life we often have to deal with an object traveling without uniform acceleration.

An example is driving with a friend in a car.

Instantaneous Acceleration is the acceleration of an object at one moment of time

Lesson 1: 1-D Kinematics Intro

Do Worksheet Problems - Acceleration

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Lesson 1: 1-D Kinematics Intro

Summary

Vocabulary: Formulas: - Displacement Δd = df - di

- Average velocity- Instantaneous velocity- Initial & Final velocity- Uniform motion- Average acceleration- Instantaneous acceleration- Vector & scalar

t

dvavg

t

va avg