Acceleration
2.2 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
Monday
 More with
 Acceleration and Data Lab
 Kinematic Equations
 Practice Problem Solving
Objectives: We Will Be Able To…
 Describe motion in terms of changing velocity.
 Compare graphical representations of accelerated and nonaccelerated motions.
 Apply kinematic equations to calculate distance, time or
velocity under conditions of constant acceleration.
Warm-Up:
1. Describe the motion of the
object in one complete
sentence.
2. Sketch the Position vs.
Time graph you think
describes the object
Velocity
 To the right is a Velocity vs.
Time (VvT) graph of an
object that starts at the
origin.
Time
Warm Up
Time
Position vs. Time
Position
Velocity
Velocity vs. Time
Time
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 Acceleration
Formula 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 Acceleration
Velocity 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
Time
Velocity
Velocity
Velocity
Velocity vs. Time Graphs
Time
Time
Positive Acceleration
Negative Acceleration
Zero Acceleration
Positive Slope
Negative Slope
Zero Slope
VvT and PvT Graphs Together
Position
Velocity
How does positive acceleration affect position?
Time
Time
VvT and PvT Graphs Together
Position
Velocity
How does positive acceleration affect position?
Time
Time
VvT and PvT Graphs Together
Position
Velocity
How does positive acceleration affect position?
Time
Time
VvT and PvT Graphs Together
Time
Velocity
Velocity
Velocity
 What do the position graphs look like for the 3 possibilities
for negative acceleration? Sketch them in your notes.
Time
Time
VvT and PvT Graphs Together
Time
Position
Position
Position
 What do the position graphs look like for the 3 possibilities
for negative acceleration? Sketch them in your notes.
Time
Time
VvT and PvT Graphs Together
 What about zero acceleration?
 Zero acceleration = no change in velocity…
 Constant velocity!
Velocity
Position
 You already know what this looks like!
Time
Time
VvT and PvT Graphs Together
 To Summarize: (p. 51)
Homework
 Due tomorrow: p. 49 #3-5
Motion with Constant Acceleration
Get 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?