Acceleration2.2 pp. 48-59

Mr. Richter

Agenda

Warm-Up Introduction to Acceleration Notes:

What is Acceleration? Calculating Acceleration Graphs of Acceleration

Review Homework Problems Practice Acceleration Graphs

Agenda Day 2 and 3

Friday More with

Kinematic Equations

Practice Problem Solving

Monday Acceleration and Data Lab

Objectives: We Will Be Able To… Describe motion in terms of changing velocity. Compare graphical representations of accelerated and

non-accelerated motions. Apply kinematic equations to calculate distance, time

or velocity under conditions of constant acceleration.

Warm-Up:

To the right is a Velocity vs. Time (VvT) graph of an object that starts at the origin.

1. Describe the motion of the object in one complete sentence.

2. Sketch the Position vs. Time graph you think describes the object

Velo

city

Time

Warm Up

Velocity vs. Time Position vs. Time

Velo

city

Time TimePosit

ion

Acceleration

What is Acceleration?

What comes to mind when I say the word acceleration?

Discuss at your tables for 1 minute and then we will discuss as a class.

What is Acceleration?

Most objects do not travel at a constant speed all of the time.

Acceleration is the rate of change of velocity. In other words:

how quickly does velocity change how long does it take to change from one velocity or

another how quickly an object speeds up or slows down

As well as: how quickly an object changes direction. More on this in later topics.

What is Accleration?

Just like displacement and velocity, acceleration has direction and magnitude (size, amount).

We consider: acceleration to the right or up to be positive, and to the left or down to be negative.

NOTE: An object does not have to be moving in the positive direction (positive velocity) to have positive acceleration, or vice versa. It only needs to be “trending” toward positive velocity.

Calculating AccelerationFormula Time!

Calculating Acceleration: Formula Acceleration is the rate of change in velocity, or how

much velocity changes with time.

Calculating Acceleration: Units

If acceleration is the rate of change in velocity [m/s] relative to time [s]…

The units for acceleration are(often): We abbreviate this verbally as “meters per second

squared”. But we really mean “meters per second per second”,

or a change in meters per second (velocity) every second (time). Therefore, 5 m/s2 really means a 5 m/s change in velocity

every second.

Practice Problem

A shuttle bus slows to a astop with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to 0.0 m/s?

Δt = 5.0 sec

Graphs of AccelerationVelocity vs. Time

Velocity vs. Time (VvT) Graphs

Position vs. Time graphs show us the velocity of an object.

Similarly, Velocity vs. Time graphs show us the acceleration of an object.

In your notes, sketch what you think the VvT graph looks like for (2 mins): Positive Acceleration Negative Acceleration No Acceleration

Velocity vs. Time Graphs

Velo

city

Time

Velo

city

Time

Velo

city

Time

Negative AccelerationNegative Slope

Positive AccelerationPositive Slope

Zero AccelerationZero Slope

VvT and PvT Graphs Together

How does positive acceleration affect position?

Velo

city

Time Time

Posit

ion

VvT and PvT Graphs Together

How does positive acceleration affect position?

Velo

city

Time Time

Posit

ion

VvT and PvT Graphs Together

How does positive acceleration affect position?

Velo

city

Time Time

Posit

ion

VvT and PvT Graphs Together What do the position graphs look like for the 3

possibilities for negative acceleration? Sketch them in your notes.

Velo

city

Time

Velo

city

TimeVe

locit

yTime

VvT and PvT Graphs Together What do the position graphs look like for the 3

possibilities for negative acceleration? Sketch them in your notes.

Time

Posit

ion

Time

Posit

ion

Time

Posit

ion

VvT and PvT Graphs Together What about zero acceleration? Zero acceleration = no change in velocity… Constant velocity!

You already know what this looks like!

Velo

city

Time Time

Posit

ion

VvT and PvT Graphs Together

To Summarize: (p. 51)

Homework

Due tomorrow: p. 49 #3-5

Motion with Constant AccelerationGet ready for formulas.

A note about Constant Acceleration Formulas

All of the following are derived from either the definition of velocity or the definition of acceleration.

Derivations are in your book on pp. 52-56. They’re not magic, but we don’t really have the time to

get into where they come from.

We will only deal with constant acceleration in this class. More advanced physics classes discuss changes in acceleration as well.

Displacement with Constant Uniform Acceleration

The amount of displacement an object experiences depends on: the initial velocity (how fast are you going when you start) the acceleration (how quickly do you change that velocity) time (how do you move while you’re changing the

velocity)

Velocity with Constant Uniform Acceleration

The final velocity depends on: the initial velocity (how fast are you going at the start) the acceleration (how quickly do you change that velocity) the time (how long do you change that velocity)

Displacement with Constant Uniform Acceleration

Combine the last two formulas and simplify…

Final Velocity after any Displacement

Another combination…

All Four Together (p.58)

Note the difference between the right and left column.

All formulas contain some information but omit others.

This is your toolbox. Each problem you solve require you to use one or more tools. You choose.

Practice Problem

a. 16 m/s b. 7.0 s

Wrap-Up: Did we meet our objectives?