Describing Motion

Objective: By the end of Chapter 2 we will know the

concepts of motion; position, displacement, velocity, and

acceleration.

Objective: By the end of Chapter 2 we will know the

concepts of motion; position, displacement, velocity, and

acceleration.

Picturing MotionPicturing Motion

Motion DiagramsMotion Diagrams

Motion Diagram - A series of images of a moving object that records its position at equal time intervals. Constant Velocity

Acceleration

Deceleration

Motion Diagram - A series of images of a moving object that records its position at equal time intervals. Constant Velocity

Acceleration

Deceleration

Particle DiagramsParticle Diagrams

Particle Diagram - The images of the motion diagram are replaced with points representing the centers of mass.Constant Velocity

Acceleration

Deceleration

An illustration...

Particle Diagram - The images of the motion diagram are replaced with points representing the centers of mass.Constant Velocity

Acceleration

Deceleration

An illustration...

Motion Diagrams

Operational DefinitionsOperational Definitions Operational Definition - Defining concepts in

terms of the procedure (operation) you used to identify them.

We defined four concepts of motion:

1) At Rest: Standing Still. No speed. Zero speed.2) Constant Velocity: Constant speed. Maintain

Speed.3) Acceleration: Increasing speed. Speeding up.4) Deceleration: Decreasing speed. Slowing down.

Operational Definition - Defining concepts in terms of the procedure (operation) you used to identify them.

We defined four concepts of motion:

1) At Rest: Standing Still. No speed. Zero speed.2) Constant Velocity: Constant speed. Maintain

Speed.3) Acceleration: Increasing speed. Speeding up.4) Deceleration: Decreasing speed. Slowing down.

How does it feel?How does it feel? How does constant velocity in a car "feel"?

Why? How does acceleration in a car "feel"? Why? How does deceleration in a car "feel"? Why?

How does constant velocity in a car "feel"? Why?

How does acceleration in a car "feel"? Why? How does deceleration in a car "feel"? Why?

How does taking a curve in a car "feel"? Why?

How does taking a curve in a car "feel"? Why?

Advanced thoughts…Advanced thoughts…

Where and When?Where and When?

Coordinate System - Deciding where to place the measuring tape and when to

start the timer.

Coordinate System - Deciding where to place the measuring tape and when to

start the timer.

Origin - Point where both variables are of value zero.

Position Vector

Position Vector: Straight line with arrow (vector) having one end fixed to a body (vector tail) and the other end attached to the origin or reference point (vector head).

Vector (arrow) from origin to the center of mass at time t.

Displacement Vector

Displacement Vector: a vector quantity that defines the distance and direction between two positions.

So what’s the difference? Position vector is from origin. Displacement is from point to point. All position vectors are displacement vectors but not all displacement vectors are position vectors.

Vectors versus Scalars

Scalar Quantity - A quantity that tells you only the magnitude of something (e.g. temperature, mass, time.)

Vector Quantity - A quantity that tells you not only the magnitude of something but also the direction.

Velocity & AccelerationVelocity & Acceleration

Velocity - Change in distance (∆x) traveled for a given change in time (∆t) .

v = Change in distance = ∆x

Change in time ∆t

Note Bene: ∆x = change in = x1-x0 or x2- x1

Velocity - Change in distance (∆x) traveled for a given change in time (∆t) .

v = Change in distance = ∆x

Change in time ∆t

Note Bene: ∆x = change in = x1-x0 or x2- x1

Velocity

Average Velocity - Change in distance (∆x) traveled for a given change in time

(∆t) .

** Will not show fluctuations in speed during travel

Average Velocity - Change in distance (∆x) traveled for a given change in time

(∆t) .

** Will not show fluctuations in speed during travel

Average Velocity

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v =Δx

Δt=x1 − x0t1 − t0

Average Speed - Ratio of total change in distance (∆x) traveled to the total change in time (∆t).

Average Speed - Ratio of total change in distance (∆x) traveled to the total change in time (∆t).

Average Speed

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v =Δx

Δt=x f − x0t f − t0

=x ft f

What is the difference?What is the difference?

Speed versus Velocity

+V=V

Scalar = MagnitudeSpeed = Magnitude

S=S

Vector = Magnitude + DirectionVelocity = Magnitude + Direction

Instantaneous velocity - Velocity at a particular “instant” of time. This is a point on the distance - time graph. (A.k.a. Velocity at time “t”). Tangent to curve at time “t”.

Instantaneous velocity - Velocity at a particular “instant” of time. This is a point on the distance - time graph. (A.k.a. Velocity at time “t”). Tangent to curve at time “t”.

Instantaneous Velocity

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v t = limΔt→0

Δx

Δt=dx

dt= slope of distance − time graph

The slope of the distance-time graph is the velocity. The slope of the distance-time graph is the velocity.

Slope of distance-time

Constant velocity Changing velocity = ?

Average Acceleration - Change in velocity (∆) traveled for a given change in

time (∆t) .

Average Acceleration - Change in velocity (∆) traveled for a given change in

time (∆t) .

Average Acceleration

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a =Δv

Δt=v1 − v0t1 − t0

Instantaneous acceleration - Acceleration at a particular “instant” of time. This is a point on the velocity-time graph. (A.k.a. acceleration at time “t”). Tangent to curve at time “t”.

Instantaneous acceleration - Acceleration at a particular “instant” of time. This is a point on the velocity-time graph. (A.k.a. acceleration at time “t”). Tangent to curve at time “t”.

Instantaneous Acceleration

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at = limΔt→0

Δv

Δt=dv

dt= slope of velocity − time graph

The slope of the velocity-time graph is the acceleration. The slope of the velocity-time graph is the acceleration.

Slope of velocity-time

Constant acceleration

Follow these steps to solve problems:

Follow these steps to solve problems:

Problem Solving

1. Read problem2. Make Diagram3. Identify Knowns4. Identify Unknowns5. Choose Formula6. Solve (and check)

***Acronym R&D Kufs

Chapter 2 Study Guide

Section 2.3 – Velocity and Acceleration

Homework and Quiz

Chapter 2 Review – 1-23 all, p. 60-61